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1905 


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BANCROFT 
LIBRARY 


THE  LIBRARY 

OF 

THE  UNIVERSITY 

OF  CALIFORNIA 


^ 


/ 


DEPARTMENT  OF  COMME^G^^ND  LABOR 


^c. 


THE  WORK 


OF  THE 


Coast  and  Geodetic  Survey 


WASHINGTON 
GOVERNMENT   PRINTING  OFFICE 

1905 


DEPARTMENT  OF  COMMERCE  AND  LABOR 


THE  WORK 


// 


OF  THE 


Coast  and  Geodetic  Survey 


WASHINGTON 

GOVERNMENT    PRINTING   OFFICE 

1905 


PREFACE. 


Leaflets,  descriptive  of  the  work  ot  the  Coast  and  Geodetic  Survey, 
were  published  as  separates  for  distribution  at  the  Louisiana  Purchase 
Exposition,  held  at  St.  Louis,  Mo.,  in  1904,  and  they  have  been 
republished  in  this  form  for  distribution  at  the  Lewis  and  Clark 
Centennial  Exposition,  at  Portland,  Oregon,  in  1905. 

It  will  be  seen  on  inspection  that  they  are  intended  to  present  con- 
cise statements  relating  to  the  origin  of  the  Survey,  to  the  general 
plan  of  its  operations,  to  the  methods  and  processes  whereby  the 
work  is  carried  on,  and  to  some  of  the  more  important  results  reached 
in  its  progress. 

Ill 


CONTENTS. 


1.  The  Coast  and  Geodetic  Survey. 

2.  Triangulation  and  Reconnaissance. 

3.  Base  apparatus. 

4.  Time,  Latitude,  Longitude,  and  Azimuth. 

5.  Terrestrial  Magnetism. 

6.  Hydrography. 

7.  Topography. 

8.  Tides  and  Tidal  Currents. 

9.  Leveling. 

10.  Coast  Pilots. 

11.  Chart  Publications. 

12.  Gravity. 

13.  Geodesv  or  Measurement  of  the  Earth. 


DEPARTMENT  OF  COMMERCE  AND  LABOR 
COAST  AND  Geodetic  Survey 

O,  H.  TITTMANN,  Superintendent 


No.  1 


THE   COAST  AND   GEODETIC  SURVEY 


To  all  nations  whope  territory  touches  the  sea  or  who  have  any 
interests  in  the  commerce  of  the  sea,  a  full  and  complete  knowledge 
of  the  coast — its  nature  and  form,  the  character  of  the  sea  bottom 
near  it,  the  locations  of  reefs,  shoals,  and  other  dangers  to  navigation, 
the  rise  and  fall  of  the  tides,  the  direction  and  strength  of  currents, 
and  the  character  and  amount  of  magnetic  disturbance— is  of  the 
greatest  moment. 

To  supply  this  knowledge  the  governments  of  the  principal  maritime 
nations  have  in  modern  times  made  surveys  of  their  coasts  by  the  most 
exact  methods. 

Some  idea  of  the  importance  to  this  country  of  such  operations  may 
be  formed  Avhen  it  is  remembered  that  the  coast  line  of  the  United 
States  and  Alaska,  measured  along  its  general  trend,  exceeds  10,000 

No.  1 


2- 

miles  in  length.  To  represent  the  actual  shore  line  which  includes  all 
the  islands,  bays,  sounds,  and  rivers  in  the  littoral  or  tidal  belt,  these 
figures  would  have  to  be  multiplied  many  times.  To  this  must  be. 
added  the  shore  line  of  Porto  Rico,  the  Hawaiian  Islands  and  the 
Philippine  Islands.  The  length  of  the  general  shore  line  of  only 
fourteen  of  the  principal  islands  of  the  latter  group  exceeds  11,000 
miles. 

On  the  recommendation  of  President  Thomas  Jefferson,  Congress  in 
1807  authorized  the  establishment  of  a  national  Coast  Survey  as  a 
bureau  under  the  Secretary  of  the  Treasury.  No  further  action  was 
taken  until  1811,  when  preparations  were  made  and  field  work  be- 
gan in  1816.  The  work  was  suspended  in  1818  and  resumed  in  1832. 
For  the  purpose  of  furnishing  geographic  positions  and  other  data  to 
State  surveys,  the  scope  of  the  Bureau  was  enlarged  in  1871  and  in 
1878  its  designation  became  the  Coast  and  Geodetic  Survey. 

In  1903  the  Bureau  was  transferred  to  the  newly  created  Depart- 
ment of  Commerce  and  Labor. 

The  plan  upon  which  it  is  at  present  organized  is  based  on  the  broad 
scientific  foundation  proposed  by  Hassler  and  approved  by  Jefferson. 
Its  present  methods  have  been  perfected  as  the  result  of  experience 
gained  in  the  field  and  office  during  the  century  of  its  existence. 

Under  the  direction  of  a  superintendent  there  are  two  great  divi- 
sions of  its  work,  the  field  and  the  office. 

In  accordance  with  the  plan  of  reorganization  of  1843,  the  work  on 
shore  was  divided  between  civilian  assistants  and  officers  of  the  Army, 
and  the  hydrographic  work  was  almost  entirely  under  charge  of  offi- 
cers of  the  Navy. 

In  1861  the  officers  of  the  Army  and  Navy  were  detached,  and  since 
that  date  no  officers  of  the  Army  have  been  assigned  to  duty  on  the 
Survey.  After  the  civil  war  the  assignments  of  officers  of  the  Navy 
gradually  increased  in  number,  so  that  the  hydrographic  work  was 
about  equally  divided  between  them  and  the  civil  assistants  during 
the  period  which  followed  until  1898,  when  the  officers  of  the  Navy 
were  finally  relieved,  and  in  1900  Congress  authorized  the  establish- 
ment of  the  Survey  on  a  purely  civil  basis. 

The  Survey  owns  a  fleet  of  eleven  steamers  and  four  schooners,  and 
a  number  of  launches. 


The  personnel  of  the  Survey  is  at  present  divided  as  follows: 

1.  Field  force,  composed  of  46  assistants,  29  aids,  8  magnetic  observ- 
ers, 4  nautical  experts,  6  tide  observers,  32  watch  officers,  engineers, 
surgeons,  deck  officers,  etc.,  and  300  enlisted  men  with  such  additional 
employees  as  are  necessary  to  insure  the  effective  work  of  field  parties 
on  shore. 

2.  Office  force,  composed  of  disbursing  agent,  chiefs  of  division, 
clerks,  computers,  draftsmen,  engravers,  instrument  makers,  printers, 
etc.,  numbering  145  persons. 

The  office  is  that  part  of  the  establishment  which  receives  the 
records,  original  sheets,  etc.,  representing  the  results  of  field  work. 
They  are  registered  and  deposited  in  the  archives  until  in  turn  they 
are  taken  up  for  examination,  computation,  and  adjustment,  prepared 
for  publication,  and  finally  published.  Charts  prepared  from  original 
surveys  are  reduced,  engraved,  electrotyped,  and  printed. 

For  the  convenience  of  administration  the  operations  of  the  main 
office  at  Washington  are  carried  on  by  eight  divisions,  each  having 
some  specified  portion  of  the  general  work  to  perform. 

There  are  suboffices  at  San  Francisco  and  Manila.  The  latter  is 
practically  a  branch  office  in  the  sense  that  the  officer  in  charge,  rep- 
resenting the  Superintendent,  has  authority  to  prepare  and  publish 
charts  and  sailing  directions  and  all  other  information  which  he  de- 
cides is  necessary  or  desirable  for  the  use  of  mariners. 

Many  of  the  field  operations  of  the  Survey  being  geodetic  in  their 
nature,  a  system  of  primary  triangulation,  together  with  the  determi- 
nation of  geographic  positions  by  means  of  astronomic  methods,  must 
furnish  the  foundation  upon  which  the  whole  rests.  On  the  Atlantic 
coast  a  chain  of  triangles  begins  at  the  eastern  boundary  of  Maine  and 
stretches  to  the  Gulf  of  Mexico.  An  extensive  system  of  triangles 
extends  across  the  continent  along  the  thirty-ninth  parallel  of  latitude, 
connecting  the  surveys  of  the  two  coasts  and  furnishing  a  basis  for  the 
surveys  of  the  thirteen  States  through  which  it  passes.  Another  tri- 
angulation system  is  being  extended  along  the  ninety-eighth  meridian. 

In  connection  with  these  principal  systems,  the  triangulation  has 
been  considerably  expanded  in  the  New  England  States,  New  York, 
and  several  Western  States,  including  California,  where  some  exception- 
ally large  figures  were  introduced.  The  longest  line  so  far  observed  is 
that  from  Mount  Helena  to  Mount  Shasta,  over  190  miles  in  length. 


A  tertiary  triangulation  for  topographic  and  hydrographic  purposes 
has  been  completed  along  the  entire  Atlantic  and  Gulf  coasts  and 
Porto  Rico,  and  practically  the  whole  of  the  Pacific  coast  except 
Alaska.  Much  progress  has  been  made  in  the  latter  Territory  and  in 
the  Philippines  by  methods  which  possess  a  sufficient  degree  of 
accuracy  for  immediate  use  and  are  capable  of  rapid  execution. 

In  the  determination  of  astronomic  positions  the  exact  methods 
originally  developed  in  the  Survey  have  been  adhered  to  and  perfected. 
The  methods  of  using  the  zenith  telescope  for  latitude  and  the  tele- 
graph for  longitude  have  been  constantly  improved. 

Incidentally  the  triangulation  and  the  astronomic  observations  con- 
nected with  it  furnish  the  most  valuable  data  for  the  determination  of 
the  figure  of  the  earth  that  has  been  contributed  by  any  one  nation. 

The  topographic  operations  have  been  mostly  restricted  to  a  narrow 
margin,  rarely  more  than  3  or  4  miles  wide,  along  the  coast  and  sur- 
rounding harbors,  bays,  and  rivers  to  the  head  of  tide  water. 

The  hydrographic  operations  have  extended  as  far  out  from  the 
coast  as  was  necessary  for  the  interests  of  navigation,  and  have  in- 
cluded all  harbors,  channels,  bays,  etc.,  as  far  as  the  work  has  gone. 

Deep-sea  soundings  have  been  made  extensively,  especially  in  and 
about  the  Gulf  Stream. 

Much  attention  has  been  given  to  tides,  and  continuous  series  of 
tidal  records  have  been  obtained  at  important  points. 

The  results  of  the  operations  of  the  Survey  in  connection  with  the 
study  of  terrestrial  magnetism  can  be  found  on  its  charts  and  in  its 
numerous  publications  on  the  subject.  In  addition  to  the  determina- 
tion of  the  magnetic  elements  at  many  widely  distributed  points  and 
their  frequent  redetermination  for  secular  variation,  special  observa- 
tions are  also  made  at  certain  base  stations,  with  the  aid  of  self- 
registering  instruments,  for  the  purpose  of  obtaining  the  record  of  the 
numerous  variations  of  the  earth's  magnetism  continually  taking  place. 

The  study  of  the  force  of  gravity  as  a  part  of  the  great  geodetic 
problem  has  received  attention  for  many  years,  and  the  Survey  has 
developed  methods  and  instruments  with  which  the  work  can  be  done 
at  a  greatly  reduced  cost,  and  with  a  high  standard  of  accuracy. 

A  network  of  precise  levels  covering,  in  a  general  way,  the  eastern 
half  of  the  United  States,  connecting  the  Atlantic  Ocean,  the  Gulf  of 


Mexico,  and  the  Great  Lakes,  has  been  run,  and  is  being  extended 
to  the  Pacific  Ocean. 

Throughout  its  history  the  Survey  has  constantly  been  called  upon 
to  determine  boundary  lines,  both  State  and  National. 

The  principal  publications  of  the  Survey  consist  of  about  500 
different  charts;  tide  tables  for  all  the  principal  and  many  of  the 
minor  ports  of  the  world;  a  monthly  edition  of  4,350  copies  of  a 
circular  known  as  "Notice  to  mariners,"  containing  notes  of  all 
changes  along  the  coast;  Coast  Pilots,  containing  minute  sailing  direc- 
tions for  all  navigable  waters  along  our  coast;  and  the  Annual  Eeport 
of  the  Coast  and  Geodetic  Survey,  which  contains  the  report  of  the 
Superintendent  on  the  conduct  of  the  work,  and  special  reports  upon 
the  various  technical  and  scientific  operations  of  the  service. 

Washington,  D.  C,  April  30,  J 904. 


o 


DEPARTMENT  OF   COMMERCE  AND   LABOR 
Coast  and  Geodetic  Survey 

O.  H.  TITTMANN,  Superintendent 


No.  2 


TRIANGULATION  AND  RECONNAISSANCE 


In  any  survey  it  is  necessary  to  know  the  relative  positions  of  some 
principal  points  of  reference  upon  which  to  base  the  work.  In  other 
words,  the  distances  and  directions  between  certain  points  must  be 
known. 

When  the  area  to  be  surveyed  is  small  or  unimportant,  the  distances 
may  be  measured  directly  upon  the  ground,  with  chain  or  tape,  and 
the  directions  may  be  obtained  by  the  use  of  a  compass  or  surveyor's 
transit.  But  when  a  survey  is  to  cover  an  extensive  territory,  or 
when  great  precision  is  desired,  this  method  is  unsatisfactory.  Aside 
from  the  difl5culties  and  delays  experienced  in  making  accurate  linear 
measurements  upon  even  moderately  level  ground,  the  natural 
obstructions,  such  as  bays,  rivers,  mountains,  and  forests,  frequently 
render  direct  measurement  impracticable.  To  overcome  these  diffi- 
culties the  method  called  * '  triangulation  "  is  employed.    It  rests  upon 

No.  2 


the  geometrical  proposition  that  if  one  side  and  the  angles  of  a  triangle 
are  known  the  remaining  sides  can  be  determined. 

A  single  line,  forming  a  side  of  one  of  the  triangles,  is  measured 
with  extreme  care.  The  angles  of  each  triangle  are. measured  and  the 
distances  between  the  points  are  then  computed,  one  from  another, 
through  the  successive  triangles,  proceeding  in  regular  order  from  the 
measured  line  or  base.  From  these  fundamental  ideas  it  is  evident 
that  the  three  stations  forming  each  triangle  nuist  be  intervisible,  and 
it  is  also  desirable  that  the  triangles  should  be  as  nearly  equilateral  as 
practicable. 

Triangulations  are  usually  classified  as  j^riynary,  secondary,  or  tertiary, 
in  accordance  with  their  relative  importance  and  the  size  of  their  indi- 
vidual triangles.  Primary  triangulation  is  the  basis  upon  which  rests 
the  accuracy  of  an  extended  survey,  and  consists  of  triangles  of  maxi- 
mum size.  Tertiary  triangulation  is  usually  composed  of  many  small 
triangles,  furnishing  the  numerous  points  of  reference  needed  for  the 
detailed  survey  of  any  locality,  while  the  term  "secondary  triangula- 
tion" is  applied  to  work  of  an  intermediate  character,  serving  to 
reduce  the  long  lines  of  the  primary  system  to  more  convenient 
dimensions. 

The  work  of  selecting  points  which  shall  fulfill  these  conditions  is 
called  Reconnaissance,  and  is  the  most  difficult  and  exacting  task  of 
an  extensive  survey.  No  two  regions  call  for  the  same  treatment,  but 
some  general  considerations  can  here  be  briefly  outlined. 

A  reconnaissance  may  be  preliminary  to  minor  triangulation  along 
the  seacoast,  a  river,  or  an  estuary,  where  but  a  moderate  degree  of 
accuracy  is  required  and  the  range  of  selection  of  points  is  limited  by 
the  purpose  for  which  the  triangulation  is  to  be  used,  namely,  the 
control  of  a  hydrographic  or  topographic  survey  along  the  shore.  Or, 
again,  it  may  have  to  do  with  the  arrangement  of  a  great  triangulation 
to  cover  a  wide  region.  In  the  latter  case  careful  study  will  be 
required  in  order  that  the  resulting  project  may  best  satisfy  all  the 
conditions.  A  reconnaissance  for  triangulation  of  the  largest  size  is  a 
matter  of  great  complexity  and  demands  great  skill,  experience,  and 
judgment.  Heavily  wooded  country  is  the  most  troublesome,  and 
makes  it  necessary  to  climb  the  tallest  trees,  or  to  raise  poles  taller  than 
the  trees,  from  which  the  distant  horizon  can  be  seen  and  such  obser- 
vations made  as  may  be  practicable. 


MOUNTAIN   TRIANGULATION   STATION. 


When  the  reconnaissance  of  a  region  has  been  completed  and  the 
stations  of  the  triangulation  have  been  selected,  the  three  angles  of 
each  triangle  are  carefully  measured.  Instruments  of  various  sizes 
and  stands  or  piers  of  different  kinds  are  employed,  according  to  the 
character  of  the  country,  the  size  of  the  triangulation,  and  the  facilities 
at  hand.  These  conditions  also  determine  the  kind  of  signals  or 
objects  to  be  used  at  the  distant  stations.  At  great  distances  the  only 
objects  which  can  be  used  are  heliotropes  by  day  and  powerful  lights 
by  night.  The  heliotrope  is  a  small  mirror  so  arranged  that  it  reflects 
the  sunlight  toward  the  observer.  During  the  past  three  years  acety- 
lene lamps  mounted  behind  a  pair  of  powerful  condensing  lenses  have 
been  used  for  night  signals. 

The  theodolites  used  in  primary  triangulation  are  instruments  with 
well-graduated  circles  from  12  to  24  inches  in  diameter.  The  circle  is 
read  to  a  second  of  arc,  or  closer,  by  three  micrometer  microscopes, 
the  mean  of  the  readings  constituting  one  observation  of  a  direction. 
Were  all  the  conditions  perfect,  a  single  careful  observation  of  each 
direction  would  be  suflBcient.  But  the  most  excellent  instruments 
have  some  defects;  the  most  careful  observers  are  liable  to  some  slight 
error;  and,  above  all,  the  line  of  sight,  passing  through  miles  of  atmos- 
phere of  variable  density  and  temperature,  is  subject  to  influences 
which  defy  analysis,  and  which  can  be  neutralized  only  by  making 
observations  under  different  conditions.  In  order  also  to  eliminate 
errors  due  to  irregular  graduation,  these  successive  observations  are 
made  on  different  parts  of  the  circle  by  shifting  it  through  a  definite 
portion  of  the  circumference  after  each  set  of  observations.  The 
number  of  such  positions  may  vary  widely  for  primary  triangulation. 

The  present  practice  is  to  use  sixteen  positions  on  the  circle,  making 
one  reading  with  the  telescope  direct  and  one  with  the  telescope 
reversed  for  each  position,  giving  sixteen  measures  of  each  direction. 

Triangulation  with  very  long  lines  is  possible  only  in  regions  of  high 
mountains,  where  the  curvature  of  the  earth  is  overcome  by  the  natu- 
ral elevations.  In  lower  country,  heavily  wooded,  or  where  moun- 
tains of  nearly  uniform  height  are  closely  crowded  together,  triangula- 
tion must  have  more  moderate  dimensions,  with  lines  from  10  to  40 
miles  long.  In  such  country  it  will  often  be  necessary  to  elevate  the 
instrument  from  20  to  150  feet  above  the  surface,  either  on  some  existing 
2 


building,  or  upon  a  structure  built  for  the  purpose.  Heliotropes  and 
lamps  can  still  be  used,  and  signal  poles  are  also  useful  in  cloudy 
weather. 

In  secondary  and  tertiary  triangulation  the  lines  may  range  down- 
ward from  20  miles  to  less  than  1  mile.  The  same  general  principles 
apply  as  in  primary  triangulation,  but  the  details  of  the  work  will 
vary  with  the  circumstances.  Heliotropes  are  rarely  used,  and  the 
angles  are  often  measured  with  theodolites  from  6  to  12  inches  in 
diameter,  and  a  smaller  number  of  measures  are  required.  After 
measuring  the  angles  the  triangle  sides  are  computed.  The  latitudes 
and  longitudes  of  all  stations  are  also  computed  by  geodetic  formulae. 

The  accuracy  attained  in  triangulation  may  be  tested  in  various 
ways.  The  sum  of  the  angles  of  a  plane  triangle  must  equal  180°,  and 
the  same  condition  holds  good  in  a  geodetic  triangle,  after  reducing  it 
to  a  plane  triangle  by  deducting  the  spherical  excess  due  to  the  figure 
of  the  earth.  The  difference,  if  any,  between  180°  and  this  corrected 
sum  is  the  error  of  closure,  which  in  the  best  work  will  average  rather 
less  than  V\  We  may  also  test  a  triangulation  by  comparing  the  com- 
puted length  of  a  line  obtained  through  a  long  chain  of  triangles  with 
an  actual  measurement  of  the  same  line.  In  the  triangulation  between 
the  Maryland  and  Georgia  base  lines,  602  miles  apart,  the  discrepancy 
was  scarcely  perceptible,  being  little  over  half  an  inch  in  a  30-mile 
line.  This  line  was  a  triangle  side  halfway  between  the  base  lines, 
and  the  comparison  was  made  by  computing  its  length  from  each  base 
line  through  the  triangulation.  Equally  small  discrepancies  have 
been  found  in  other  triangulations,  and  the  method  may  be  considered 
practically  exact. 

Various  improvements  made  in  the  methods  of  primary  triangulation 
by  the  Coast  and  Geodetic  Survey  have  resulted  in  the  speed  of  the  work 
in  1902-3  being  more  than  doubled,  as  compared  with  earlier  work  of 
the  same  kind  in  the  United  States  and  the  present  work  in  foreign 
countries. 

The  cost  of  the  work  has  also  been  greatly  reduced  without  percep- 
tible loss  of  accuracy. 

Washington,  D.  C,  April  SO,  1904. 

o 


DEPARTMENT  OF  COMMERCE  AND   LABOR 
Coast  and  Geodetic  Survey 

O.  H.  TITTMANN,  Superintendent 


No.  3 


BASE  APPARATUS 


A  base  in  geodesy  is  a  line  actually  measured  upon  the  ground  for 
the  purpose  of  determining  the  dimensions  of  a  series  of  connected  tri- 
angles, of  one  of  which  it  forms  a  side.« 

In  an  extended  triangulation  there  will  probably  be  several  bases, 
which  serve  as  checks  upon  each  other  when  all  have  been  connected 
by  computation  through  the  system  of  triangles.  Their  number  will 
depend  upon  the  plan  adopted  for  the  work,  upon  the  means  available 
for  the  measurements,  and  upon  the  nature  of  the  country,  which  may 
or  may  not  afford  suitable  sites  at  convenient  places.  Very  broken 
ground  is  unsuitable  for  base  measures,  though  moderate  slopes  offer 
no  serious  obstacles. 


No.  3 


a  See  leaflet:  Triangulation  and  Reconnaissance. 


It  is  evident  that  the  length  of  a  base  should  be  obtained  with  a 
high  degree  of  precision,  since  any  error  in  its  length  is  multiplied  as 
many  times  as  that  length  is  contained  in  the  whole  extent  of  the 
work.  This  demands  a  degree  of  care  and  refinement  far  surpassing 
ordinary  needs,  and  for  this  reason  various  devices  have  at  different 
times  been  contrived  for  the  special  purpose  of  extremely  precise  meas- 
urement.    Such  arrangements  are  collectively  called  base  apparatus. 

The  attainment  of  absolute  accuracy  in  the  measurement  of  a  base 
depends  upon  certain  essentials  which  must  be  secured,  whatever  the 
form  of  apparatus  used.  These  are:  (1 )  A  knowledge  of  the  length  of 
the  apparatus  in.  standard  measure  at  the  moment  of  use;  (2)  the 
inclination,  or  deviation  of  the  apparatus  from  the  horizontal;  (3)  the 
measure  of  the  fractional  distances  which  may  occur  at  the  end  of 
any  section.  The  alignment  of  the  bars  in  the  direction  of  the  base 
line  can  be  made  sufficiently  perfect,  and  therefore  no  correction  for 
deviations  from  the  vertical  plane  of  the  base  needs  consideration. 

Of  the  three  requisites  just  mentioned,  the  first  is  far  the  most  diffi- 
cult of  attainment  and  is  the  only  one  which  needs  special  consideration 
in  this  paper.  The  length  of  a  bar  or  tape  varies  with  its  temperature. 
Hence,  in  order  to  obtain  correct  results,  that  temperature  must  be 
known  with  absolute  accuracy  throughout  the  measurement,  and  that 
again  is  very  difficult  to  accomplish. 

EARLY  FORMS  OF  APPARATUS. 

Among  the  earlier  forms  of  base  apparatus  were  metallic  chains, 
wooden  rods,  and  glass  tubes.  Wooden  rods  have  been  used,  under 
special  circumstances,  as  late  as  1857,  and  the  chain  is  still  frequently 
used  in  ordinary  land  surveying,  though  long  discarded  in  work  of 
precision.  As  will  be  seen  a  little  later,  however,  metallic  tapes  and 
wires,  which  differ  less  in  principle  than  in  details,  have  been  much 
used  in  recent  geodetic  work  and  seem  likely  to  be  still  more  frequently 
employed  in  the  future. 

CORRECTIONS    FOR   TEMPERATURE. 

The  early  forms  just  mentioned  were  gradually  supplanted  by 
metallic  bars,  which  apparently  were  first  used  in  1788,  in  Italy,  and 


in  1798,  in  France.  With  their  use,  the  changes  in  length  of  the  bars 
due  to  variations  of  temperature  at  once  became  a  most  important  sub- 
ject for  consideration. 

Two  main  difficulties*  present  tliemselves  in  this  connection;  first, 
to  determine  tlie  precise  change  in  the  length  of  a  given  bar  for  a  given 
change  of  temperature;  and  second,  to  determine  the  exact  tempera- 
ture of  the  bar  at  any  given  time.  In  practice,  the  latter  requirement 
is  much  the  more  troublesome,  since  under  the  conditions  of  exposure 
inseparable  from  base  measurement  it  is  practically  impossible  to 
determine  by  thermometers,  with  absolute  accuracy,  the  actual  tem- 
perature of  a  bar  unless  that  temperature  is  invariable. 

Four  different  methods  have  at  various  times  been  followed  in  the 
attempt  to  ayoid  the  errors  due  to  varying  and  uncertain  temperature. 

The  first  method  was  to  use  for  the  measuring  rods  materials  which 
were  only  slightly  affected  by  temperature  changes,  such  as  wood  or 
glass,  as  already  mentioned.  Other  considerations  then  prevented  the 
success  of  such  systems,  but  it  is  probable  that  in  the  near  future  the 
nearly  invariable  alloy  of  steel  and  nickel,  discovered  in  France  and 
there  called  ^' invar,''  may  come  into  use  for  this  purpose.  In  fact, 
base  bars  of  this  metal  have  already  been  made  and  are  undergoing 
tests  as  to  their  qualities. 

The  second  method  is  to  ascertain  the  temperature  of  the  metallic 
bar  or  tape  by  means  of  mercurial  thermometers  suitably  applied  and 
then  to  correct  the  measured  length  accordingly  by  means  of  the  care- 
fully determined  coefficient  of  expansion  of  the  bar  or  tape.  The 
weak  point  of  this  method  is  the  impossibility,  noted  above,  of  cer- 
tainly securing  absolute  equality  of  temperature  between  the  bar  or 
tape  and  the  mercurial  thermometer. 

The  third  method  is  to  use  compound  bars,  in  which  parallel  rods 
of  two  metals  possessing  quite  different  rates  of  expansion,  as  platinum 
and  copper  or  steel  and  brass,  for  example,  replace  the  single  rod  of 
one  metal.  The  ends  of  the  rods  being  provided  with  suitable  scales 
or  other  devices  for  intercomparison,  the  relative  displacements  due  to 
temperature  changes  may  be  measured.  Such  an  arrangement,  often 
called  the  Borda  scale  from  the  name  of  its  originator,  is,  of  course,  a 
form  of  thermometer,  and  from  the  readings  taken  at  any  time  the 


length  of  the  compound  bar  can  be  computed.  This  principle  of 
differential  expansion  is  applied,  in  different  ways,  in  several  of  the 
modern  forms  of  apparatus. 

In  Borda's  apparatus,  used  by  Delambre  in  1798,  the  strips  of  copper 
and  platinum  which  formed  the  measuring  bar  were  firmly  connected 
at  one  end,  while  free  to  expand  or  contract  at  the  other.  In  Porro's 
apparatus,  sixty  years  later,  the  components  of  steel  and  copper  were 
united  at  the  middle,  while  in  the  Eimbeck  "duplex"  apparatus  of 
the  present  day  the  parallel  tubes  of  steel  and  brass  are  capable  of 
independent  motion. 

A  somewhat  different  application  of  the  principle  is  found  in  the 
"compensation  apparatus,"  used  by  Colby  in  Ireland,  in  1827,  and  by 
Borden  in  Massachusetts,  in  1831.  Colby's  apparatus  has  also  been 
used  in  England  and  in  India.  In  each  of  these  the  differential 
expansion  was  utilized  to  produce  a  bar  of  invariable  length  in  the 
following  manner:  The  parallel  rods  of  iron  and  brass  are  firmly  cori- 
nected,  midway  of  their  length,  while  near  each  end  a  transverse 
metal  strip,  the  "compensation  tongue,"  pivoted  to  each  rod,  projects 
to  one  side.  The  proportions  of  the  rods  and  their  attachments  are  so 
arranged  that  the  distance  between  two  points  marked  upon  the  pro- 
jecting ends  of  the  transverse  strips  remains  invariable,  or  nearly  so, 
whatever  the  temperature.  This  apparatus,  however,  has  not  been 
found  entirely  satisfactory,  especially  in  India,  the  compensation  not 
being  absolutely  reliable. 

The  elaborate  apparatus  constructed  for  the  United  States  Coast 
Survey  in  1845  combines  the  principles  of  Borda's  measuring  rods, 
the  Colby  compensation  tongue,  and  the  contact  lever  introduced  by 
the  Russian  astronomer,  Struve,  with  marked  improvements  in  their 
application.  The  length  of  the  compound  bar  was  supposed  to  be  in- 
dependent of  temperature,  but,  as  in  the  Colby  apparatus,  the  com- 
pensation was  not  absolutely  exact,  slightly  different  results  being 
obtained  with  rising  and  with  falling  temperatures  and  the  bars  were 
therefore  standardized  under  each  condition.  Much  excellent  work 
was  done  with  this  apparatus,  although  it  is  no  longer  in  use. 

The  fourth  method,  and  the  only  perfect  solution  of  the  problem,  is 
to  eliminate  temperature  corrections  by  maintaining  the  bar  at  a  con- 
stant temperature,  when  its  length  will,  of  course,  be  invariable.     The 


well-known  fact  that  melting  ice  affords  a  uniform  standard  of  tem- 
perature points  the  way  to  the  attainment  of  this  end  and  the  appli- 
cation of  the  principle  in  the  iced  bar  apparatus  of  the  Coast  and 
Geodetic  Survey,  designed  by  Woodward,  leaves  little  to  be  desired 
on  the  score  of  precision. 

TYPES   OF   BASE   APPARATUS. 

All  forms  of  apparatus  may  be  divided  into  two  principal  classes, 
namely:  (1)  Those  which  use  but  a  single  measuring  unit,  whether 
chain,  tape,  or  metallic  bar;  and  (2)  those  which  employ  two  or 
more  separate  units. 

With  apparatus  of  the  first  type  the  measurement  of  the  base  pro- 
ceeds by  repeated  applications  of  the  single  unit,  the  ends  of  its  suc- 
cessive lengths  being  marked  in  the  case  of  a  tape  upon  posts  or  tripods 
firmly  planted  in  the  ground  and  in  the  case  of  a  bar  by  powerful 
microscopes  mounted  upon  firm  supports.  Measures  of  this  type  are, 
in  general,  line  measures,  i.  e. ,  their  lengths  are  defined  by  lines  upon 
their  surfaces.  In  the  case  of  a  bar  these  are  microscopic  lines 
engraved  upon  small  polished  disks  of  gold,  silver,  or  platinum  inlaid 
in  the  bar  near  its  ends. 

With  apparatus  of  the  second  type  the  measurement  proceeds  by 
the  alternate  application  of  the  several  units  of  measurement,  end  to 
end,  either  in  actual  contact  or  separated  by  a  small  interval,  which 
is  carefully  measured  by  some  suitable  device.  Bars  of  this  type  are, 
in  general,  end  measure  bars,  i.  e.,  their  lengths  are  defined  by  their 
ends. 

Bars  of  either  type  are  usually  supported  upon  stable  tripods,  or  even 
more  permanent  supports,  provided  with  suitable  arrangements  for 
controlling  the  alignment  and  the  inclination  of  the  bars. 

It  is  obvious  that  the  principle  of  Borda's  device  may  be  applied  to 
apparatus  of  either  type  by  the  simultaneous  use  of  two  metals  possess- 
ing quite  different  coefficients  of  expansion.  A  subdivision  into 
monometallic  and  himetallic  forms  therefore  becomes  necessary. 

The  limits  of  this  paper  will  not  permit  even  a  brief  description  of 
the  various  forms  of  base  apparatus  which  have  been  used  in  the  dif- 
ferent geodetic  surveys,  but,  speaking  generally,  it  may  be  stated  that 
most  of  the  European  surveys  favor  the  bimetallic  forms,  that  of  Porro, 


6 

for  example,  of  the  first  or  single  bar  type,  or  those  of  Borda,  Bessel, 
and  Brunner,  of  the  second  or  multiple  bar  type.  In  Spain,  however, 
while  the  central  base  of  Madridejos  was  measured  with  a  compound 
bar  of  copper  and  platinum,  on  the  Porro  system,  some  later  bases  of 
verification  have  been  measured  with  an  iron  bar  designed  by  General 
Ibafiez,  and  in  Russia  the  monometallic  forms  devised  by  Struve  and 
Tenner  were  exclusively  used  for  many  years.  The  most  recent 
Russian  bases,  however,  have  been  measured  with  the  bimetallic  ap- 
paratus of  Jiiderin.  In  this  system  a  wire  of  steel  and  another  of 
brass,  each  25  meters  long  and  2  millimeters  in  diameter,  are  stretched 
between  tripods  under  a  tension  of  10  kilograms.  Each  wire  carries 
a  divided  scale  near  one  end  for  measuring  the  exact  distance  to  the 
forward  tripod.  The  tension  is  measured  by  a  spring  balance.  Two 
bases  were  measured  in  1888  with  this  apparatus  and  another  in  1894. 
It  seems  to  possess  a  degree  of  precision  sufficient  for  geodetic  pur- 
poses and  is  at  the  same  time  capable  of  rapid  use,  as  much  as  3,500 
meters  having  been  easily  measured  per  day.  The  apparatus  is  also 
simple,  portable,  and  inexpensive. 

APPARATUS   NOW    IN    USE    IN   THE    COAST    AND   GEODETIC   SURVEY. 

The  foregoing  general  observations  lead  to  the  main  purpose  of  this 
paper,  the  description  of  the  apparatus  and  methods  now  employed 
by  the  Coast  and  Geodetic  Survey.  In  the  recent  work  four  princi- 
pal forms  have  been  used,  namely: 

(1)  The  so-called  iced  bar,  a  monometallic  single-bar  system. 

(2)  The  duplex  apparatus,  a  bimetallic  multiple-bar  system. 

(3)  The  secondary  apparatus,  a  monometallic  multiple-bar  system. 

(4)  The  tape  apparatus,  a  monometallic  single-unit  system. 

ICED   BAR   APPARATUS. 

The  measuring  unit  is  a  steel  bar  5  meters  long,  that  length  being 
defined  by  microscopic  lines  engraved  upon  the  polished  surfaces  of 
small,  inset,  platinum-iridium  plugs  near  the  ends  of  the  bar  and  in 
its  neutral  axis,  to  permit  which  arrangement  the  upper  part  of  each 
end  is  cut  away  for  a  short  distance.  While  in  use  it  is  supported 
within  a  metallic  trough  tilled  with  melting  ice,  which  keeps  the  bar 
at  constant  temperature.     ITncertainties  due  to  varying  temperature 


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7 

are  therefore  entirely  avoided.  The  trough  inclosing  the  bar  is  sup- 
ported upon  a  carriage  movable  upon  a  track  built  for  the  purpose. 
The  successive  positions  of  the  ends  of  the  bar  are  fixed  by  powerful 
microscopes  firmly  attached  to  stout  posts  solidly  planted  in  the  ground 
and  such  refinements  are  used  at  every  step  of  the  process  of  measure- 
ment that  an  extraordinary  degree  of  accuracy  is  obtained. 

Measurements  with  this  apparatus  are  deemed  in  the  United 
States  too  slow  and  costly,  however,  to  be  advisable  for  an  entire 
base,  and  the  most  recent  practice  of  the  Coast  and  Geodetic  Survey 
is  to  use  it  for  measuring  with  great  precision  a  distance  of  100  meters, 
near  and  parallel  to  the  base  about  to  be  measured.  This  distance  of 
100  meters  then  becomes  a  field  standard  for  the  careful  testing  and 
comparison,  under  actual  field  conditions,  of  the  apparatus  intended 
for  the  actual  base  measurement.  When  a  number  of  bases  are  to  be 
measured  in  the  same  season,  this  field  standardization  is  effected  at 
the  first  and  last  bases  of  the  series.  For  the  purpose  of  establishing 
these  accurate  field  standards  the  value  of  the  iced  bar  apparatus  can 
hardly  be  overestimated. 

DUPLEX  APPARATUS. 

The  duplex  apparatus,  as  the  name  implies,  has  two  separate  meas- 
uring rods  in  each  compound  bar,  one  being  made  of  steel  and  the 
other  of  brass.  These  rods  are  tubular,  instead  of  being  solid  as  usual, 
and  the  thickness  of  their  walls  is  based  on  the  specific  heat  and  con- 
ductivity of  each  metal.  To  give  the  tubes  equal  capacities  foT  absorb- 
ing and  radiating  heat  they  are  plated  with  nickel.  These  tubular 
rods  are  so  arranged  that  an  independent  measure  is  conducted  with 
each,  giving  for  any  measured  distance  two  results,  one  in  terms  of 
the  steel,  the  other  in  terms  of  the  brass  component.  By  means  of 
attached  scales  direct  comparisons  between  the  two  may  be  made 
whenever  desired.  The  difference  between  the  two  measures  deter- 
mines the  average  temperature  of  the  two  rods  and,  by  means  of  the 
ratio  of  the  expansions  of  brass  and  of  steel,  the  corrections  which 
will  reduce  the  measures  to  standard,  without  any  reference  to  mer- 
curial thermometers.  Each  compound  bar  is,  however,  provided  with 
three  such  thermometers,  and  a  single  measurement  will  therefore 
yield  thr«e  results,  a  duplex  and  two  separate  thermometric  results. 


8 

Though  these  results  are  perhaps  not  absolutely  independent,  they 
afford  valuable  checks  upon  tfie  reliability  of  the  measurement.  It 
will  be  seen  that  the  great  difference  between  this  and  other  bimetallic 
types  is  that  instead  of  making  the  comparison  between  the  compo- 
nents for  each  successive  5-meter  bar,  in  which  case  the  changes  are 
of  course  minute,  the  measurement  is  continued  for  a  considerable 
distance  between  comparisons,  500  or  1,000  meters,  for  example,  giv- 
ing in  effect  the  comparison  between  steel  and  brass  bars  of  that  length, 
with  a  considerable  increase  of  precision  in  its  accomplishment.  This 
apparatus  has  been  used  upon  ten  bases  recently  measured  in  the 
United  States,  and  is  an  undoubted  success,  giving  results  of  a  high 
order  of  precision  at  a  moderate  expense. 

SECONDARY   APPARATUS. 

The  secondary  apparatus  of  the  Coast  and  Geodetic  Survey  is  a 
simple  monometallic  type  possessing  a  considerable  degree  of  precision. 
The  rods  are  of  steel  and,  for  the  purpose  of  checking  radiation,  are 
inclosed  in  massive  woodeii  bars,  from  which  they  project  a  little  at 
each  end.  Temperatures  are  determined  by  mercurial  thermometers, 
two  for  each  bar,  which  are  inclosed  in  the  wooden  casing,  with  their  ■ 
bulbs  in  contact  with  the  steel  rod,  one  near  each  end.  The  contact 
slide  device,  used  also  on  the  duplex  bars,  was  first  designed  for  this 
apparatus.  To  secure  the  best  results  with  this  apparatus,  the  meas- 
urement should  be  equally  divided  between  period?  of  rising  and  of 
falling  temperature. 

TAPE  APPARATUS. 

steel  tapes  have  been  used  with  marked  success  in  measuring  twelve 
recent  bases  in  the  United  States.  In  each  case,  however,  they  have 
been  standardized,  under  field  conditions,  by  comparison  with  a  teat 
base  carefully  measured  with  the  iced  bar  or  have  been  used  in  con- 
nection with  the  duplex  or  the  secondary  apparatus.  On  the  nine 
most  recent  bases  independent  measures  were  made  with  four  differ- 
ent tapes,  two  of  which  were  50  and  two  100  meters  long.  In  recent 
work  of  precision  in  the  United  States,  all  tape  measurements  have 
been  made  at  night,  it  having  been  found  that  mercurial  thermome- 
ters will  not  accurately  indicate  the  temperature  of  the  tape  in  day- 
light.    The  steel  tapes  now  used  are  either  50  meters  (164  feet)  or 


9 

100  meters  (328  feet)  long.  They  are  6.34  millimeters  (0.25  inch) 
wide  and  about  0.47  millimeter  (0.019  inch)  thick.  During  the 
measurements  they  are  supported  at  intervals  of  25  meters  (82  feet), 
the  intermediate  supports  being  wire  nails  driven  horizontally  into 
the  sides  of  stakes  previously  arranged  for  that  purpose.  The  succes- 
sive positions  of  the  forward  end  of  the  tape  are  marked  upon  copper 
strips  secured  to  the  tops  of  suitable  posts,  which  are  previously 
aligned  at  the  proper  distances.  In  the  measurement,  a  tension  of  15 
kilograms  (33.1  pounds)  is  applied  to  the  tape  by  a  lever,  the  amount 
of  the  tension  being  determined  by  a  spring  balance.  "With  this 
tension,  the  sag  of  the  tape  between  supports  is  very  slight,  and  a 
high  degree  of  accuracy  in  the  measurement  of  the  tension  is  there- 
fore unnecessary.  The  temperature  of  the  tape  is  determined  by  two 
mercurial  thermometers  attached  to  the  tape  near  its  ends. 

Mention  must  here  be  made  of  a  very  promising  application  of  the 
thermophone  to  the  determination  of  the  temperature  of  a  steel  tape, 
suggested  by  Professor  Burton,  of  the  Massachusetts  Institute  of  Tech- 
nology. By  this  device  the  temperature  of  a  tape  is  obtained  by  the 
application  of  the  principle  of  the  differential  variations,  with  varying 
temperatures,  of  the  electrical  resistances  of  steel  and  German  silver, 
the  tape  for  this  purpose  being  made  one  arm  of  a  Wheatstone  bridge. 

It  seems  probable  that  when  this  apparatus  has  been  further  im- 
proved, to  make  it  more  convenient  in  use  and  less  liable  to  injury  by 
accident,  it  may  enable  tape  measurements  of  precision  to  be  made  by 
day  instead  of  by  night,  and  thus  considerably  facilitate  such  operations. 
It  is  also  probable  that  the  nearly  invariable  alloy  of  steel  and  nickel, 
previously  mentioned,  may  play  an  important  part  in  future  measure- 
ments, wires  of  that  metal  having  already  been  used  in  the  measure- 
ment of  base  lines  by  the  Jiiderin  system.  It  seems  evident  that  base 
measurement  by  tape  apparatus  will  become  more  and  more  common 
and  that  by  this  means  the  number  of  geodetic  bases  will  be  very 
greatly  increased.  The  following  observations  will  be  interesting  in 
this  connection. 

PRECISION   AND   ECONOMY   OF    MEASUREMENT. 

The  accuracy  attainable  with  either  bars  or  tapes  falls  well  within  the 
limits  required  for  even  the  most  accurate  triangulation.     Experience 


10 

has  shown  that  the  judicious  use  of  tapes  easily  admits  of  repeating  a 
measurement  with  no  greater  discrepancy  than  about  one-twelfth  inch 
per  mile,  or  about  1  part  in  760,000,  and  that  the  duplex  apparatus 
admits  of  remeasuring  a  line  with  a  discrepancy  not  exceeding  about 
one-sixteenth  inch  per  mile,  or  about  1  part  in  1,000,000.  These 
figures  represent  average  discrepancies  for  sections  of  a  base,  each  a 
mile  in  length,  and,  in  the  case  of  continuous  measurements,  these  may 
be  assumed  to  cancel  each  other,  in  part  at  least.  Hence  the  accuracy 
of  a  base  line  several  miles  in  length  may  be  expected  to  be  propor- 
tionatelv  still  greater  than  that  mentioned. 

While  steel  tapes  give  nearly  the  same  degree  of  accuracy  as  the 
duplex  apparatus,  the  cost  of  measuring  a  base  with  any  good  bar 
apparatus  is  nearly  three  times  as  great  as  for  tape  measurements. 

In  Appendix  3  of  the  Coast  and  Geodetic  Survey  Report  for  1901 
may  be  found  a  detailed  statement  in  regard  to  the  measurement  of 
nine  primary  base  lines  by  one  party  in  six  months,  with  a  high 
degree  of  accuracy,  showing  a  very  successful  application  of  business 
methods  to  the  operations  of  geodesy. 

Washington,  D.  C,  Aj^ril  SO,  1904- 


DEPARTMENT  OF  COMMERCE  AND   LABOR 
Coast  and  Geodetic  Survey 

O.  H.  TITTMANN,  Superintendent 


No.  4 


TIME,  LATITUDE,  LONGITUDE,  AND  AZIMUTH 


Time  determinations  as  made  by  the  Coast  and  Geodetic  Survey 
are  incidental  to,  and  necessary  in  connection  with,  observations  of 
latitude,  longitude,  and  azimuth.  Astronomic  determinations  of  lati- 
tude and  longitude  are  necessary  in  connection  with  a  survey  to  place 
it  in  its  proper  position  on  the  earth's  surface.  Astronomic  obser- 
vations of  azimuth  serve  to  determine  the  true  directions  of  lines 
fixed  by  a  survey. 

TIME. 

Time  may  be  determined  by  observations  on  the  sun  or  stars  with 
any  instrument  which  will  measure  their  altitude  or  indicate  their 
meridian  passage.  For  this  purpose  sextants  or  altazimuth  instru- 
ments are  generally  used  for  approximate  determinations,  and  a  transit 
adjusted  to  the  meridian  for  refined  work.    With  the  transit,  a  chrono- 

No.  4 


graph  is  frequently  used  for  recording  the  observations.  The  tele- 
scope usually  has  from  five  to  eleven  vertical  lines,  which  are  placed 
in  the  common  focus  of  the  eyepiece  and  object  glass,  the  center  line 
being  adjusted  to  the  optical  axis  of  the  telescope  and  set  in  the 
meridian. 

When  ready  for  observations,  the  observer  sets  the  telescope  at  the 
proper  elevation  to  observe  the  passage  of  the  star  across  the  meridian, 
and  records  on  the  chronograph  the  transit  over  each  line  by  inter- 
rupting the  circuit  with  an  observing  key  held  in  the  hand  and  elec- 
trically connected  with  the  chronograph,  on  which  a  break-circuit 
chronometer  is  making  a  continuous  record.  The  chronograph  sheet 
is  read  by  means  of  a  scale. 

LATITUDE. 

Latitudes  of  an  inferior  grade  may  be  determined  with  a  sextant  or 
an  altazimuth  instrument  by  observations  on  the  sun  or  stars,- but 
determinations  of  the  first  order  are  usually  made  by  observations  on 
the  stars  with  a  zenith  telescope.  The  principle  on  which  this  method 
depends  is  the  measurement,  with  a  micrometer,  of  small  differences 
.of  zenith  distance  of  two  stars,  nearly  equidistant  from  but  on  oppo- 
site sides  of  the  zenith.  The  telescope  is  set  to  the  mean  zenith  dis- 
tance of  the  two  stars,  one  of  which  passes  above  and  the  other  below 
the  center  of  the  iield.  These  two  stars,  forming  a  pair,  should  cul- 
minate within  from  one  to  twenty  minutes  of  each  other,  and  they  are 
bisected  bv  the  movable  micrometer  line  as  thev  reach  the  meridian. 

In  the  past  the  use  of  from  fifteen  to  twenty-five  pairs  observed  on 
three  nights  has  been  considered  necessary  for  a  good  determination. 

LONGITUDE. 

The  longitude  of  a  place  may  be  determined  by  observations  of  the 
eclipses  of  the  satellites  of  Jupiter,  of  solar  eclipses,  of  moon  culmina- 
tions, of  occultations  of  stars,  and  by  transporting  chronometers  with 
varying  degrees  of  accuracy.  The  most  accurate  results  are  obtained 
by  determining  the  difference  of  time  between  the  desired  positions 
by  the  telegraphic  method.  The  local  time  must  be  determined  in 
the  usual  manner  at  the  two  places  on  the  same  nights  (6  nights  for 


work  of  primary  importance)  and  a  comparison  of  the  chronometers 
must  be  made  on  each  night  by  using  a  telegraph  line  between  the 
places. 

Each  static  (1  should  be  supplied  with  a  transit,  a  break-circuit 
chronometer,  a  chronograpli,  and  a  set  of  telegrap^h  instruments. 
Two  time  sets  must  be  observed  at  both  stations  each  night,  and 
between  the  observations  the  two  chronometers  must  be  compared 
over  the  telegraph  line  In';  means  of  chronometer  signals,  which  are 
arbitrary  breaks  made  by  the  observers  alternately,  and  recorded  on 
both  chronographs.  The  comparison  of  chronometers  only  requires 
about  three  minutes.  The  transmission  time  of  the  electric  current  is 
derived  by  sending  signals  in  both  directions,  and  the  personal  equa- 
tion of  the  observers  is  eliminated  by  the  interchange  of  observers 
after  half  the  work  is  completed,  or  is  obtained  by  direct  observations, 
if  the  work  is  not  of  primary  importance. 

In  longitude  work  of  the  first  order,  observations  should  be  made 
each  night  on  twenty  stars  to  determine  the  local  time  at  the  stations. 
When  the  transits  are  equipped  with  Repsold  self- registering  micro- 
meter eye  pieces,  the  observations  are  free  from  personal  equation. 
In  using  this  micrometer  the  star  is  kept  constantly  bisected  by  the 
movable  micrometer  line  during  its  passage  across  the  field  of  the  tele- 
scope, and  its  position  is  automatically  recorded  at  regular  intervals. 

AZIMUTH. 

Azimuths  are  of  different  grades,  according  to  the  purposes  for  which 
they  are  required. 

For  exploration,  reconnaissance  or  magnetic  observations  theodo- 
lites with  horizontal  circles  from  3  to  6  inches  in  diameter  are  used  to 
observe  on  the  sun  or  tne  north  star. 

For  tracing  meridian  lines  or  for  tertiary  triangulation  theodolites 
with  horizontal  circles  from  6  to  10  inches  in  diameter  are  used  in 
connection  with  a  circumpolar  star. 

For  the  principal  triangulation,  12  to  20  inch  circles,  which  are  read 
to  single  seconds  by  micrometer  microscopes,  are  needed  to  produce 
an  accuracy  commensurate  with  the  requirements  of  the  work.  Only 
circumpolar  stars  are  observed   to  determine  high-grade  azimuths. 

3  . 


Accurate  time  is  required  for  this  class  of  work,  except  when  the 
observations  are  made  at  elongation. 

A  terrestrial  mark  is  used  in  connection  with  all  azimuth  observa- 
tions. 

For  fuller  details  refer  to  Chauvenet's  Spherical  and  Practical 
Astronomy,  or  to  the  Report  of  the  United  States  Coast  and  Geodetic 
Survey,  1898,  Appendix  No.  7. 

Washington,  D.  C,  April  30,  1904. 


o 


DEPARTMENT  OF  COMMERCE  AND   LABOR 

COAST  AND  Geodetic  Survey 

O.  H.  TITTMANN,  Superintendent 


No.  5 


TERRESTRIAL  MAGNETISM 


In  the  "Plan  for  the  reorganization  of  the  survey  of  the  coast,  as 
adopted  by  a  board  convened  on  the  30th  of  March,  1843,  by  direction 
of  the  President  of  the  United  States,"  explicit  provision  is  made  for 
the  making  of  "all  such  magnetic  observations  as  circumstances  and 
the  state  of  the  annual  appropriations  may  allow,"  and  Congress,  in 
its  annual  appropriations,  distinctly  recognizes  the  importance  of  this 
feature  of  the  work  of  the  Coast  and  Geodetic  Survey. 

With  the  advancing  years  the  demands  for  practical  information 
from  surveyors  and  mariners  became  so  heavy  that  on  July  1,  1899, 
an  inspector  was  detailed  for  general  charge  of  the  field  work  and  the 
discussion  of  results,  which  had  previously  been  a  function  of  the 
Computing  Division  of  the  Office,  was  placed  in  charge  of  the  Division 
of  Terrestrial  Magnetism,  which  was  created  for  that  purpose. 

No.  5 


A  magnetic  or  compass  needle  does  not  point  "  true  to  the  pole,"  as 
the  old  saying  would  have  it,  but  instead  makes  an  angle  with  the 
true  north  and  south  line,  as  was  first  discovered  by  Columbus,  this 
angle  varying  according  to  the  location  of  the  place  where  the  compass 
is  mounted.  Thus,  in  the  United  States,  in  the  extreme  northeastern 
part  of  Maine,  the  compass  needle  points  21°  west  of  north,  while  in 
the  northwestern  part  of  the  State  of  Washington  it  points  23°  east  of 
north,  a  change  of  44°  from  one  end  of  our  country  to  the  other  (see 
Chart  of  Lines  of  Equal  Magnetic  Declination  for  1900) .  There  are 
portions  of  the  earth  where  the  "  north  "  end  of  the  needle  points  due 
east  or  due  west,  and  even,  for  certain  regions  between  the  magnetic 
north  pole  and  the  geographic  north  pole,  due  south. 

In  view,  then,  of  the  use  of  the  compass  by  the  surveyor  to  locate 
land  surveys,  by  the  mariner  to  guide  him  over  trackless  seas,  and  by 
the  traveler  to  pilot  him  in  unfrequented  regions  of  the  earth,  it  be- 
comes the  first  object  of  magnetic  surveys  to  determine  the  amount  by 
which  the  compass  direction  differs  from  the  true  direction,  and  to 
publish  the  quantities  in  such  a  form  that  those  interested  may  at  a 
glance  be  able  to  extract  the  desired  information.  The  Chart  of  Lines 
of  Equal  Magnetic  Declination  for  the  United  States,  based  on  over 
5,000  determinations  in  different  parts  of  the  country,  is  a  specimen 
of  the  form  now  generally  adopted  for  giving  this  information. 

Not  only  does  the  needle  not  generally  point  due  north,  as  already 
shown,  but  the  amount  of  its  departure  therefrom  is  continually  under- 
going change  from  hour  to  hour,  from  day  to  day,  and  from  year  to 
year.  At  London,  for  example,  the  needle  changed  its  direction  from 
11°  east  in.l580  to  24°  12^  west  in  1812,  a  change  of  35°  in  232  years. 
A  street  a  mile  long  laid  out  in  London  during  the  year  1580  in  the  direc- 
tio7i  indicated  by  tJie  compass  at  that  time  would  have  had  its  northern 
terminus  slx-tentlts  of  a  mile  too  far  east,  according  to  the  compass  direction 
af  1812.  At  the  present  time,  at  London,  the  needle  points  about 
16°. 5  west. 

In  this  country  the  rate  of  change  in  the  compass  direction  is  not 
as  large  as  at  London,  nevertheless  it  is  of  sufhcient  magnitude  to 
seriously  affect  the  magnetic  bearings  of  boundary  lines.  Thus,  at 
Baltimore,  the  needle  pointed  in  1670  about  6°  6^  west;  in  1802,  39^ 
west,  and  in  1900,  5°  west:     A  street  a  mile  long  laid  out  in  Baltimore  in 


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1670,  so  as  to  run  in  the  direction  indicated  by  the  compass  at  that  time,  would 
have  had  its  northern  terminus  one-tenth  of  a  mile  too  far  west  in  1802. 

At  St.  Louis,  at  the  time  of  the  Louisiana  purchase,  the  compass 
needle  pointed  about  7|°  east,  and  it  now  points  about  5°  east. 

Even  in  the  course  of  a  day,  from  8  a.  m.  to  2  p.  m.,  the  fickle  needle 
changes  its  direction  by  an  amount  sufficient  to  be  taken  into  account. 
This  amount,  according  to  the  season  of  the  year,  may  cause  a  dis- 
crepancy at  the  terminus  of  a  line  a  mile  long  run  by  the  coinpass  in 
the  morning  and  rerun  in  the  afternoon  of  from  5  to  20  feet. 

Again,  at  times  the  needle's  direction,  by  some  subtile  force,  is 
abruptly  changed.  This  is  the  case  during  magnetic  storms  which 
make  their  influence  felt  over  a  large  portion  of  the  globe  at  practically 
the  same  instant  of  time.  Thus,  in  November,  1882,  during  the  period 
of  maximum  sun  spot  activity,  occurred  a  magnetic  storm  which 
caused  the  needle  at  Los  Angeles,  Jalifornia,  to  change  its  direction  by 
more  than  a  degree  and  a  third.  At  the  same  time  General  Greely, 
at  Lady  Franklin  Bay,  in  the  Arctic  region,  noted  a  deflection  of  20°  48^. 
Frequently  these  magnetic  storms  are  accompanied  by  brilliant  dis- 
plays of  polar  lights.  There  are  in  addition  many  minor  fluctuations, 
depending  upon  the  position  of  the  sun  and  the  moon  with  reference 
to  the  earth  and  to  each  other. 

It  is  possible  to  portray  the  state  of  the  earth's  magnetic  condition, 
as  represented  by  magnetic  maps,  only  lor  a  definite  moment  of  time. 
The  tides,  the  trade  winds,  while  subject  to  definite,  periodic  fluctua- 
tions, nevertheless  will  not  change  their  general  character  for  thousands 
of  years,  but  a  few  years  suffice  to  materially  change  and  make  useless 
a  cartographic  representation  of  the  magnetic  forces.  It  is  of  great 
importance,  therefore,  to  provide  for  a  continuous  record  of  the  count- 
less fluctuations  of  the  magnetic  needle.  It  is  then  possible  always  to 
bring  our  magnetic  charts  up  to  date  and  to  provide  the  surveyor  and 
mariner  with  the  precise  amount  of  change  between  any  two  given 
dates.  This  necessitates  the  establishment  of  certain  base  stations, 
where  are  mounted  sensitive  magnetic  instruments,  which  photo- 
graphically record,  day  and  night,  the  variations  or  changes  of  the 
magnetic  forces. 

There  are  at  present  five  of  these  stations,  situated  as  follows:  At 
Cheltenham,  Maryland;  at  Baldwin,  Kansas;  at  Sitka,  Alaska;  at 
Vieques,  Porto  Rico,  and  near  Honolulu,  Hawaii. 


The  Coast  and  Geodetic  Survey  has  made  an  exhaustive  and  careful 
compilation  of  the  available  data  for  the  past  three  centuries  as 
obtained  from  various  sources,  and  the  practical  information,  which  it 
is  in  the  position  to  furnish  in  reply  to  inquiries  from  lawyers  and  sur- 
veyors, is  regarded  as  final  and  authoritative  throughout  the  country. 
It  can  thus  be  of  material  assistance  to  landowners  in  the  prevention 
of  costly  litigations. 

The  practical  application  of  magnetic  data  is,  however,  not  entirely 
limited  to  a  knowledge  of  the  direction  of  the  compass  needle.  The 
mariner  with  the  modern  iron  ship  now  in  use  carries  with  him  a  con- 
tinuous source  of  disturbance,  so  that  his  uncompensated  compass  will 
fail  to  give  the  true  magnetic  direction  for  the  ship's  position.  It  is 
therefore  necessary  to  apply  correcting  devices  which  to  a  large  extent 
counteract  the  ship's  magnetic  influence.  These  mechanical  devices 
are  not,  however,  entirely  compensatory  for  all  the  places  a  ship  is 
likely  to  be  in,  owing  to  the  changing  character  of  the  ship's  own 
magnetism,  and  so  the  mariner  must  determine  a  table  of  corrections 
(the  so-called  deviation  table)  for  different  localities  and  for  all  posi- 
tions and  directions  of  the  ship's  head.  For  this  purpose  a  knowledge 
of  the  dip  of  the  magnetic  needle  and  the  intensity  of  the  magnetic 
force  are  essential.  The  electrician,  the  geologist,  and  the  physicist 
likewise  desire  a  knowledge  of  these  quantities.  They  are,  further- 
more, essential  in  ascertaining  the  precise  laws  underlying  the  varia- 
tions of  the  earth's  magnetism. 

A  complete  magnetic  survey,  therefore,  embraces  the  determinations 
of  the  three  magnetic  elements,  declination  (variation  of  the  compass), 
dip,  and  intensity,  and  their  changes  from  time  to  time  over  land  and 
ocean  areas  as  well.  Special  magnetic  instruments  are  being  used  for 
the  magnetic  work  at  sea. 

One  practical  result  of  a  magnetic  survey  is  the  establishment  of 
meridian  lines  near  county  seats  for  the  purpose  of  enabling  the  sur- 
veyors to  test  and  verify  their  compasses. 

Washington,  D.  C,  April  30,  1904. 


o 


DEPARTMENT  OF  COMMERCE  AND   LABOR 

Coast  and  Geodetic  Survey 

O.  H.  TITTMANN,  Superintendent 


No.  6 


HYDROGRAPHY 


Hydrographic  surveying  is  the  process  of  determining  the  shape  of 
portions  of  the  earth's  surface  which  Ue  beneath  the  water  and  of 
recording  the  resuhs  of  such  determinations  in  form  to  be  utihzed 
in  the  construction  of  charts.  It  delineates  with  accuracy  the  sub- 
merged contour  lines  of  channels,  banks,  and  shoals.  Work  along  the 
shore  and  in  harbors  and  rivers  is  preceded  by  other  processes  of  sur- 
veying, to  which  it  is  closely  allied,  and  upon  which  depend  the  accu- 
racy of  the  final  result. 

These  processes  are,  first,  triangulation,  which  gives  points  on  land 
from  which  to  determine  the  position  of  the  soundings  taken;  and, 
second,  topography,  which  provides  the  delineation  of  the  shore  line, 
or  wharf  lines,  locates  the  rocks  that  show  above  the  water;  and  the 
limits  of  dry  shoals  and  banks.  These  data  are  placed  in  their  proper 
relation  to  each  other  on  paper  by  means  of  a  suitable  projection.    This 

No.  6 


projection  is  prepared  by  a  draftsman  on  a  scale  determined  by  the 
minuteness  with  which  the  siiljmerged  features  are  to  be  mapped.  A 
scale  of  jo^oo  (which  means  that  10,000  feet  in  nature  are  represented 
by  1  foot  on  the  projection)  is  well  adapted  for  the  survey  of  most 
harbors. 

This  2^'rojection  shows  the  geographic  position  of  the  points  which 
have  been  determined  by  triangulation.  These  points  correspond  in 
position  on  the  projection  to  certain  marks  on  the  ground  suitable  to 
observe  upon  in  locating  the  positions  of  the  soundings,  such  as  church 
spires,  chimneys  of  buildings,  peculiarly  shaped  rocks  or  trees,  and 
signals  built  over  triangulation  stations. 

When  a  sufficient  number  of  signals  and  objects  are  available,  and 
•d  tide  gauge  or  tide  staff  has  been  erected  at  some  point  in  the 
vicinity  of  the  work,  the  next  step  is  to  "run  the  lines  of  soundings." 
Having  decided  where  a  line  is  to  begin,  the  boat  is  moved  to  that 
point.  Two  observers,  with  sextant  in  hand,  the  recorder,  witli  a 
watch  or  clock  and  record  book,  and  the  leadsman,  with  his  "lead 
line,"  take  their  respective  positions.  The  officer  in  charge  directs 
the  recorder  to  make  a  note,  say,  as  follows:  "Line  begins  at  angle 
/  1,  about  20  meters  from  shore,  south  of  Fleck's  Point;  course  about 
east."  The  observers  measure  the  angles  between  three  signals  on 
shore  and  read  the  angles  measured;  the  leadsman  gets  a  cast  of  the 
lead  and  calls  out  the  number  of  feet  or  fathoms,  and  the  recorder 
records  all  these,  with  the  time  when  the  boat  begins  to  move.  The 
boat  starts  ahead  and  does  not  stop  again  until  the  end  of  the  line  is 
reached.  Other  j^airs  of  angles  are  taken  by  the  observers  at  three  or 
four  minute  intervals,  or  as  frequently  as  necessary,  each  set  of  angles 
locating  the  position  of  the  boat  at  the  instant  of  observation.  At  the 
end  of  the  line  a  final  set  is  taken.  The  boat  is  then  moved  to  a  posi- 
tion at  the  beginning  of  a  new  line.  Where  the  depths  are  changing 
rapidly,  the  soundings  are  taken  as  frequently  as  possible,  and  the 
time  of  each  sounding  may  be  noted  to  seconds;  but  where  the  bottom 
is  comparatively  level  the  soundings  are  preferably  taken  at  equal 
intervals  of  time. 

When  practicable,  the  lines  of  soundings  are  run  on  ranges — that  is, 
with  the  boat  in  the  same  straight  line  with  two  objects  on  shore. 

While  the  boat  has  been  running  the  lines  of  soundings  the  water, 


in  all  proV)ability,  has  not  maintained  the  same  level,  owing  to  the 
rise  or  fall  of  the  tide.  Each  sounding  must  therefore  be  corrected  for 
the  height  of  the  tide  at  the  time  it  was  taken,  so  as  to  reduce  all  to  a 
common  plane.  The  plane  of  reference  adopted  by  the  Survey  for  its 
charts  of  the  Atlantic  and  Gulf  coasts  is  that  of  "Mean  low  water," 
which  is,  roughly  speaking,  a  mean  reading  of  all  the  low  waters 
observed  on  the  tide  staff  for  as  long  a  series  as  practicable,  but  usually 
not  shorter  than  one  lunar  month.  The  reading  of  mean  low  water 
on  the  staff  Vicing  known,  and  observations  of  the  height  of  the  tide 
having  been  made  at  intervals  of  five  or  ten  minutes  while  the  boat 
was  sounding,  it  is  easy  to  apply  this  tidal  correction.  In  order  to 
preserve  the  height  of  the  plane  of  reference,  a  permanent  tidal  bench 
mark  is  established  on  shore  and  the  height  of  this  plane  is  carried  to 
it  by  leveling.  Descriptions  of  these  1)ench  marks  are  preserved  in 
the  archives  of  the  office.  In  deep-sea  work,  offshore,  the  tidal 
reduction  is  not  applied  to  the  soundings. 

The  Coast  and  Geodetic  Survey  requires  that  in  smooth,  shoal  water 
the  reduced  soundings  on  lines  crossing  each  other  shall  not  differ 
more  than  Ih  per  cent  of  the  depth. 

At  the  end  of  each  day's  work,  the  results  are  graphically  trans- 
ferred to  the  "projection."  Every  position  of  the  boat  corresponding 
to  any  pair  of  angles  measured  on  any  three  points  on  shore  is  plotted 
by  means  of  a  three-arm  protractor.  This  method  of  plotting,  it  \\  ill 
be  observed,  is  merely  a  graphic  solution  of  the  three-point  problem. 

The  successive  positions  of  the  sounding  boat  being  plotted,  and  the 
number  and  time  intervals  of  the  soundings  and  their  number  being 
shown  in  the  record,  it  becomes  an  easy  matter  to  space  the  sound- 
ings accurately  between  the  positions.  The  result  is  practically  the 
same  as  though  the  boat's  position  had  been  instrumentally  deter- 
mined at  each  sounding. 

Hydrographic  surveys  of  the  character  described  develop  the  slopes 
of  the  bottom,  but  in  regions  like  the  cofist  of  Maine  and  Alaska, 
where  there  are  many  isolated  rocks  and  ledges  on  the  bottom,  or  like 
the  coast  of  Florida,  Porto  Rico,  and  the  Philippines,  fringed  with 
coral  reefs,  and  many  coral  heails,  the  work  has  frequently  to  be 
supplemented  by  special  examinations  where  soundings  on  the  regular 
lines  shoaler  than  the  surrounding  depths  give  indications  that  there 


may  be  yet  shoaler  water.  Examinations  of  this  character  have  been 
greatly  facihtated  in  late  years  by  the  attachment  under  the  vessel  of 
a  device  designed  to  give  the  vessel  any  draft  of  water  up  to  6  fathoms, 
and  now  known  as  the  ''Channel  sweep."  This  device  will  find  rocks 
that  the  lead  line  has  failed  to  develop.  The  sweep  is  also  used  to 
verify  channels  that  have  been  marked  out  through  reefs,  or  areas  of 
broken  ground. 

The  method  used  in  deep-sea  sounding  differs  from  the  foregoing. 
The  leadsman  is  replaced  by  a  sounding  machine,  and  the  line  by  a 
fine  steel  piano  wire  coiled  on  a  drum,  the  depth  being  obtained  by 
recording  the  number  of  revolutions  of  the  drum  while  paying  out. 
The  "lead"  is  replaced  by  a  solid  spherical  shot  weighing  about  100 
pounds,  which  is  detached  automatically  from  the  wire  on  reaching 
the  bottom.  While  the  sounding  ship  remains  in  sight  of  land  the 
method  for  determining  its  position  is  similar  to  that  explained  above, 
but  when  out  of  sight  of  land  the  position  is  obtained  by  astronomic 
observations  and  the  ship's  log. 

Great  accuracy  is  demanded  of  the  hydrographer,  even  in  water  so 
deep  that  there  is  no  possible  danger  of  the  largest  ship  afloat  striking 
bottom,  because  the  hydrography  on  a  mariner's  chart  has  a  twofold 
object:  First,  to  indicate  to  the  navigator  the  hidden  perils  which  he 
must  avoid;  and  second,  to  display  the  configuration  of  the  bottom  so 
truly  that  by  the  use  of  the  lead  he  may  fix  his  position  relative  to 
those  perils,  or,  when  offshore,  determine  his  distance  from  land. 

For  details  of  the  theory  and  practice  of  hydrographic  surveying  the 
inquirer  is  referred  to: 

Coast  and  Geodetic  Survey  reports. 

General  Instructions  for  Hydrographic  Work,  Coast  and  Geodetic 
Survey. 

Chauvenet's  Astronomy. 

Jeffer's  Surveying. 

Howell's  Marine  Surveying. 

Washington,  D.  C,  Aj^ril  30,  1904. 

o 


DEPARTMENT  OF   COMMERCE  AND   LABOR 

Coast  and  Geodetic  Survey 


O.  H.  TITTMANN,  Superintendent 


No.  7 


TOPOGRAPHY 


A  topographic  map  is  one  on  which  the  natural  and  artificial  features 
of  the  country  are  represented  in  their  proper  geographic  positions  by 
conventional  symbols. 

The  two  most  important  symbols  on  maps,  where  they  occur,  are  the 
shore  line,  or  boundary  between  land  and  water,  and  contour  lines. 
which  are  lines  of  equal  elevation  above  a  selected  plane,  such  as  the 
sea  level,  A  contour  is  in  fact  a  representation  of  wdiat  the  shore  line 
would  be  if  the  level  of  the  water  were  to  rise  to  the  elevation  indi- 
cated by  the  particular  contour. 

In  order  to  show^  the  undulations  of  the  ground,  contour  lines  are 
drawn  for  some  constant  vertical  interval — 20  feet,  for  instance.  On 
large-scale  maps  they  have  superseded  the  representation  of  heights 
by  hachures  or  shade  lines,  which  only  picture  the  configuration  of 

No.  7 


the  country,  without  furnishing   the   niean^,  as  the  contours  do,  of 
stating  in  terms  of  some  hnear  unit  the  difference  of  elevation. 

In  reading  a  map  one  is  able  to  tell  the  nature  of  the  country  from 
the  various  symbols — whether  it  is  high  "or  low,  rugged  or  gently 
undulating,  by  the  number  and  arrangement  of  the  contours  or 
hachures — and  whether  it  is  marshy  or  sandy,  wooded  or  rocky,  and 
so  on. 

A  topographic  map  is  particularly  valuable  for  the  study  of  the 
physical  conditions  relating  to  engineering  projects  in  general,  such  as 
the  preliminary  location  of  railroads  and  highways,  the  problems 
relating  to  water  supply  and  drainage,  etc.  It  serves  as  a  basis  for 
directing  military  moveuients  and  planning  military  works  of  defense. 
Combined  with  hydrography,  it  forms  a  chart  on  which  is  shown  the 
relation  of  land  to  water  for  purposes  of  navigation  and  the  improve- 
ment of  harbors  and  waterways. 

Charting  the  coasts  of  the  United  States  is  the  chief  function  of  the 
Coast  and  Geodetic  Survey,  and  topography  is  necessarily  included  as 
one  of  the  important  features  of  its  work. 

A  topographic  survey  has  for  its  objecu  the  collection  of  data  for  the 
construction  of  a  topographic  map.  The  character  of  the  map  in 
regard  to  accuracy,  scale,  and  fullness  of  detail  depends  on  the  purpose 
which  it  is  intended  to  serve.  Military  topographic  sketches  are  fre- 
quently made  by  using  a  pocket  compass,  the  stride  of  the  observer's 
horse  serving  to  estimate  the  distance.  More  elaborate  methods  are 
used  where  greater  accuracy  is  required  and  greater  detail  is  desired. 

Different  topographic  methods  require  the  use  of  various  instru- 
ments and  may,  for  the  purpose  of  description,  be  classed  under  four 
heads,  from  the  fact  that  each  method  is  identified  with  some  particular 
instrument  or  combination  of  instruments  with  which  the  principal 
part  of  the  work  is  done. 

1.  With  a  chain  or  steel  tape  and  level,  by  what  may  be  called  the  checker- 
board system. — The  whole  area  is  subdivided  into  rectangles  by  a 
system  of  distances  measured  wdth  a  chain  or  steel  tape  and  marked 
by  pegs  whose  elevations  are  determined  with  a  level  and  rod.  The 
positions  and  elevations  of  the  pegs  having  been  plotted,  the  contours 
are  drawn  on  the  plan  with  reference  to  them,  and  all  other  details 
are  located  by  measureuients  from  them.     This  method  is  best  adapted 


for  small  areas  where  work  of  construction  is  shortly  to  follow  the 
survey. 

The  ordnance  survey  of  Great  Britain  is  made  ))y  traversing  the 
country  with  a  network  of  straight  lines  measured  with  a  chain,  the 
accuracy  of  the  work  being  controlled  by  starting  each  line  from  one 
triangulation  point  and  ending  at  another.  Offsets  are  measured  from 
the  line  wherever  it  is  necessary  to  locate  details.  The  elevations  of 
a  number  of  points  on  the  ground  are  determined  by  the  level,  and 
the  contours  are  sketched  with  reference  to  these  after  the  rest  of  the 
details  have  been  plotted.  This  is  the  simplest  of  all  instrumental 
methods  in  the  field,  but  it  is  not  efficient  where  there  is  little  detail 
or  where  the  ground  is  unsuitable  for  chaining. 

2.  With  transit  and  stadia. — This  method  is  a  development  of  the 
preceding  one.  The  country  is  likewise  traversed  by  lines,  but  the 
slow,  laborious  process  of  chaining  is  discarded  for  the  quicker  one  of 
reading  the  distances  through  the  telescope  of  the  transit  on  the  stadia 
rod  held  at  any  desired  point,  and  the  lines  may  have  any  direction. 
The  level  is  also  dispensed  with,  as  the  height  of  any  point  can  be 
determined  by  computation  when  its  distance  is  known  and  the  verti- 
cal angle  to  it  is  observed.  A  vertical  circle  is  attached  to  the  transit 
for  this  purpose.  All  the  names  of  the  objects  sighted  upon,  as  well 
as  the  distances  and  angles  to  them,  are  entered  in  a  notebook, 
together  with  sketches  of  the  locality  to  assist  the  draftsman  to  inter- 
pret the  notes. 

3.  With  the  camera. — Surveys  can  be  made  with  an  ordinary  land- 
scape camera,  but  there  are  many  advantages  in  having  one  especially 
designed  for  the  purpose.  The  essential  feature  of  this  method  con- 
sists in  occupying  a  sufficient  number  of  camera  stations  to  fully  cover 
the  territory  to  be  mapped,  so  that  every  topographic  detail  of  impor- 
tance may  be  photographed  from  at  least  two  stations.  This  is  the 
most  rapid  of  all  instrumental  methods  in  the  field,  since  a  great  deal 
of  topographic  material  can  be  gathered  photographically  in  a  short 
time.  It  has  the  serious  drawback  that  for  areas  abounding  in  detail 
the  plotting  becomes  overwhelming. 

By  the  three  foregoing  methods  the  map  is  constructed  in  the  office; 
by  the  following  method  its  construction  is  coincident  with  the  field 
work. 


4.  With  the  plane  table  and  stadia. — This  is  the  principal  method  used 
for  topographic  work  by  the  Coast  and  Geodetic  Survey.  For  this 
purpose  the  plane  table  i:-»  a  universal  instrument.  All  the  necessary 
operations  for  producing  a  map  are  executed  with  it  in  the  field 
from  the  country  as  a  model.  Other  instruments  may  at  times  be 
employed  as  auxiliaries,  but  in  general  it  alone  fulfills  all  require- 
ments. Owing  to  the  rapidity  with  which  results  are  obtained  by  the 
method  of  graphic  triangulation,  and  the  facility  the  plane  table 
affords  the  topographer  for  determining  his  position  at  an  unknown 
point  by  the  graphic  solution  of  the  three-point  problem,  and  in  the 
effective  use  of  the  stadia,  it  is  an  instrument  peculiarly  fitted  for 
delineating  coast  topography,  which  includes  such  features  as  out- 
lying islands  and  ledges,  inaccessible  rocky  bluffs,  and  large  marsh 
areas  intersected  by  numerous  streams. 

In  the  experience  of  the  Coast  and  Geodetic  Survey,  derived  from 
surveying  operations  covering  the  coast  line  of  the  United  States  and 
Alaska,  over  10,000  miles  in  length  measured  along  its  general  trend, 
the  plane  table  has  proved  to  be  the  most  comprehensive  and  effective 
mapping  instrument. 

Washington,  D.  C,  April  80,  1904. 


o 


DEPARTMENT  OF  COMMERCE  AND   LABOR 

Coast  and  Geodetic  Survey 

O.  H.  TITTMANN,  Superintendent 


No.  8 


TIDES  AND  TIDAL  CURRENTS 


To  one  who  for  the  first  time  visits  the  seacoast,  the  continual  varia- 
tion of  the  water  level  due  to  the  tides  and  the  tidal  currents  which 
accompany  this  variation  possess  a  novel  and  unfailing  interest.  This 
is  especially  the  case  in  a  region  where  the  tide  has  a  large  vertical 
range,  thus  producing  many  curious  changes  in  the  aspect  of  the  shore. 
Broad  fiats  or  ragged  ledges  may  be  left  bare  at  low  water,  over  which 
boats  sail  freely  at  high  tide,  and  land  masses  which  are  peninsulas 
at  one  stage  of  the  tide  become  islands  at  another.  Even  to  one  long 
accustomed  to  these  phenomena  there  is  an  element  of  the  solemn  and 
mysterious  in  this  vast  and  irresistible  j^ulsation  of  the  waters,  coming 
in  from  the  mighty  depths  of  the  great  ocean. 

Here,  too,  the  mathematician  and  the  physicist  find  problems  of 
absorbing  interest  and  of  far-reaching  application.     From  the  time  of 

No,  8 


Sir  Isaac  Newton,  who  in  1687  laid  the  foundation  for  the  modern 
researches,  the  subject  has  received  the  attention  of  many  brilHant 
minds,  and  Daniel  Bernouilli,  Euler,  Laplace,  Whewell,  Airy,  Kelvin, 
Ferrel,  G.  H.  Darwin,  Harris,  and  others  have  investigated  the  theory 
of  the  tides.  These  investigations  have  aided  in  determining  the 
moon's  mass  and  the  mutual  relations  of  the  earth  aud  the  moon 
and  furnish  evidence  of  the  motion  of  the  earth's  axis  of  rotation 
relatively  to  the  geographic  poles. 

While  the  disturbing  forces  of  the  sun  and  the  moon  are  universally 
accepted  as  causing  the  tides,  there  is  much  to  be,  desired  in  the  way 
of  showing  how  these  forces  actually  cause  the  observed  motions. 
These  forces,  acting  horizontally  rather  than  vertically,  are  the  same 
which  deflect  the  plumb  line  from  the  mean  vertical.  By  their 
repeated  action  portions  of  the  sea  of  the  proper  depth  and  dimensions 
are  caused  to  oscillate  in  a  manner  analogous  to  the  vibration  of  a 
pendulum.  A  phenomenon  of  a  similar  nature  is  observed  in  certain 
lakes,  where  oscillations  known  as  seiches  when  once  started  continue 
for  some  time,  the  period  of  the  oscillations  depending  upon  the  dimen- 
sions of  the  lake. 

Nor  are  the  tides  of  merely  general  or  theoretical  interest.  The 
question  of  a  foot  or  two  in  depth  on  a  dangerous  shoal  may  involve 
both  lives  and  property  upon  a  passing  vessel,  while  the  commercial 
prosperity  of  a  port  may  depend  upon  the  depth  at  both  high  and 
low  water  or  upon  the  way  in  which  the  scouring  effect  of  the  tidal 
current  serves  to  preserve  its  channels. 

Any  investigation  of  the  tides,  whether  for  theoretical  or  practical 
application,  requires  a  basis  of  fact,  and  this  can  be  furnished  only  by 
careful  observations  of  the  actual  phenomena  during  considerable 
periods  of  time.  Long  series  of  observations  are  necessary  because 
the  tides  are  very  complex  phenomena,  being  modified  by  all  influ- 
ences acting  upon  the  earth  from  without,  as  well  as  by  those  arising 
upon  the  earth  itself  (such  as  winds,  earthquakes,  and  variations  of 
the  atmospheric  pressure),  by  irregularities  in  the  coast  line,  by  the 
eccentric  distribution  of  the  land  masses,  and  by  the  varying  depth  of 
the  sea.  A  sufficient  number  of  observations  is  therefore  needed  to 
eliminate  as  far  as  possible  the  effects  of  temporary  influences  and  to 


permit  the  external  forces  to  run  through  one  of  their  great  cycles,  in 
order  that  a  harmonic  analysis  may  disclose  the  various  elements 
which  go  to  make  up  the  tide. 

While  the  vertical  motion  of  the  water  surface  is  called  the  tide,  the 
horizontal  motion  of  the  water  itself  is  properly  called  the  tidal  current 
or  tidal  stream,  and  is  often  of  even  greater  practical  importance  in  navi- 
gation. While  the  rise  or  fall  of  the  tide  in  a  given  period  may  be  prac- 
tically uniform  in  amount  and  nearly  simultaneous  at  widely  separated 
points  within  quite  an  extensive  area,  the  currents  which  accompany 
the  change  will  vary  widely  within  the  same  region,  being  modified 
by  every  outline  of  the  shore  and  by  every  irregularity  of  the  bottom. 
Further  than  this,  the  time  at  which  the  tidal  current  changes  its 
direction,  as  from  flood  to  ebb  or  the  reverse,  by  no  means  necessarily 
coincides  with  the  time  at  which  the  tide  begins  to  fall  or  to  rise. 
Indeed,  it  would  be  more  nearly  correct  to  say  that  these  times  gener- 
ally differ,  the  difference  varying  from  a  few  minutes  to  as  much  as 
three  hours  in  some  localities.  Not  only  does  the  tidal  current  vary 
both  in  force  and  in  direction  in  different  parts  of  the  same  sheet  of 
water,  but  at  any  one  point  of  observation  wide  variations  are  noted 
at  different  stages  of  the  tide,  so  that  a  current  which  at  a  certain  time 
mns  with  moderate  force  along  the  axis  of  a  channel  may  perhaps  an 
hour  or  two  later  set  with  great  force  directly  across  some  dangerous 
shoal. 

It  will  be  readily  seen  that  tidal  currents  require  careful  considera- 
tion, and  that  many  difficulties  present  themselves  in  the  way  of 
obtaining  and  of  collating  sufficient  observations  to  be  able  to  i^redict 
their  direction  and  velocity  at  any  particular  time.  Fortunately,  in 
the  neighborhood  of  the  land,  where  such  currents  are  most  likely  to 
cause  disaster,  there  are  usually  landmarks  or  artificial  aids  to  naviga- 
tion, by  careful  attention  to  which  a  shipmaster  or  pilot  may  safely 
guide  his  vessel. 

The  Coast  and  Geodetic  Survey,  as  an  organization  charged  with 
tne  important  duties  of  the  preparation  of  correct  charts  and  coast 
pilots,  has  carried  on  from  very  early  days  in  its  history  the  obser- 
vation and  discussion  of  tides  and  tidal  currents. 

Observations  of  the  height  of  the  tide  are  usually  made  either  upon 


a  simple  graduated  staff  or  else  by  a  self-registering  gauge.  The  latter, 
which  is  always  employed  in  places  where  a  long  series  of  observations 
is  desired,  is  a  simple  but  ingenious  combination  of  a  clock  with  a 
recording  apparatus,  in  which  a  pencil,  controlled  in  lateral  position  by 
the  elevation  of  the  water,  traces  an  undulatory  curve  upon  a  long  strip 
of  paper  which  moves  slowly  at  right  angles  to  the  direction  of  motion 
of  the  pencil  and  is  regulated  in  its  progress  by  the  clock,  which  con- 
trols the  a})paratus. 

Washington,  D.  C,  April  SO,  1904. 


o 


DEPARTMENT  OF  COMMERCE  AND   LABOR 

Coast  and  Geodetic  Survey 

O.  H.  TITTMANN,  Superintendent 


No.  9 


LEVELING 


Leveling  is  the  operation  of  determining  differences  of  elevation 
between  any  two  points  on  the  surface  of  the  earth.  The  determina- 
tion of  such  differences,  or  relative  elevations,  is  of  primary  import- 
ance for  many  of  the  purposes  for  which  surveys  are  intended,  and 
from  them  may  readily  be  obtained  so-called  "absolute  elevations" 
above  any  particular  point  or  surface  of  reference  which  may  be  se- 
lected. The  mean  level  of  the  sea  is  the  surface  of  reference  most 
commonly  used  for  the  determination  of  heights,  but  others  arbitrarily 
selected  are  frequently  employed  for  special  purposes. 

The  two  principal  methods  now  in  use  in  the  Coast  and  Geodetic 
Survey  for  the  determination  of  elevations  are  by  precise  spirit  level- 
ing and  by  the  measurement  of  vertical  angles.  The  first  is  the  most 
accurate  method  known;  the  second  is  of  a  lower  de._re  '  of  accuracy, 
but  suffices  for  many  purposes. 

No.  9 


The  instrument  used  in  the  first  method  consists  essentially  of  a 
telescope  suitably  mounted  on  a  portable  tripod  and  carrying  a  deli- 
cate spirit  level,  so  that  it  may  be  quickly  and  readily  j)laced  in  a  hori- 
zontal position.  Graduated  rods  are  held  at  t\v5  points,  the  instrument 
being  usually  placed  midway  between  them.  The  telescope  is  sighted 
first  on  one  rod  and  then  on  the  other.  The  difference  of  the  readings 
of  the  rods  is  the  difference  of  height  between  the  two  points.  The 
length  of  sight  is  usually  short  and  should  not  exceed  150  meters  for 
accurate  work.  By  repeating  the  operation  at  successive  stations  the 
difference  of  elevation  of  widely  separated  points  may  be  determined. 

Various  types  of  instruments  have  been  used  for  precise  spirit  level- 
ing, some  of  them  being  nearly  like  the  Y  level  used  extensively  by 
engineers  on  construction  work  and  others  differing  widely  from  it. 
The  principal  characteristics  which  distinguish  the  form  of  precise 
level  now  in  use  in  the  Coast  and  Geodetic  Survey  are  the  irreversi- 
bility of  the  telescope  and  level,  the  absence  of  Y's,  the  rigid  fasten- 
ing of  the  level  vial  to  the  telescope  and  its  close  juxtaposition  to  the 
latter,  in  the  barrel  of  which  it  is  countersunk;  the  use  in  the  con- 
struction of  the  telescope,  and  adjacent  parts,  of  a  nickel-iron  alloy 
having  a  very  small  coefficient  of  expansion;  the  protection  of  the  level 
vial  and  the  middle  part  of  the  telescope  from  sudden  and  unequal 
changes  of  temperature  by  incasing  them  in  an  outer  tube;  and  an 
arrangement  by  which,  withont  any  change  of  the  observer's  position, 
the  level  bubble  can  be  clearly  seen  by  his  left  eye  at  nearly  the  same 
instant  in  which  the  distant  rod  is  observed  through  the  telescope  by 
his  right  eye. 

It  has  been  found  that  one  of  the  principal  sources  of  error  in  some 
of  the  precise  leveling  of  the  past  was  due  to  unequal  changes  of  tem- 
perature in  the  telescope  and  parts  connecting  it  with  the  level  vial. 
The  momentary  changes  in  the  relative  positions  of  the  level  vial  and 
telescope  produced  by  these  temperature  changes,  though  microscopic 
in  magnitude,  were  yet  suflScient  to  introduce  appreciable  errors  into 
the  leveling  on  long  lines.  The  particular  nickel-iron  alloy  used  in 
the  construction  of  the  new  level  expands  less  than  one-fourth  as 
much  as  brass  for  a  given  increase  of  temperature.  This,  together 
with  the  fact  that  the  level  is  mounted  as  close  as  possible  to  the  line 
of  sight,  gives  a  very  high  degree  of  stability  to  the  relation  between 


the  two,  which  is  quite  the  most  important  point  to  be  secured  in  a 
precise  levehng  instrument. 

A  line  of  precise  levels  is  always  run  twice,  usually  in  opposite  direc- 
tions, and  in  case  of  disagreement  of  the  results  beyond  prescribed 
limits  between  adjacent  bench  marks,  the  leveling  is  repeated.  Per- 
manent points  called  bench  marks  are  established  at  short  intervals, 
so  that  the  work  may  thus  be  frequently  checked.  For  the  leveling 
done  during  the  last  two  years  the  maximum  discrepancy  allowed 
between  two  measurements  on  a  section  1.6  kilometers  (1  mile)  long 
is  5  millimeters,  or  one-fifth  of  an  inch.  For  sections  of  other  lengths 
the  discrepancy  allowed  is  made  proportional  to  the  square  root  of  the 
length. 

A  much  more  severe  test  of  the  accuracy  of  the  leveling  is  obtained 
from  the  closures  of  large  circuits,  50,  100,  or  1000  miles  in  circum- 
ference. Elevations  being  carried  from  one  point  continuously  in  one 
direction  around  the  circuit,  the  computed  elevation  for  the  starting 
point  on  closing  the  circuit  should  agree  with  that  assumed  for  it  at 
the  start  if  there  are  no  errors  in  the  leveling. 

In  the  network  of  precise  leveling,  which  now  covers  in  a  general 
way  the  eastern  half  of  the  United  States,  there  are  50  such  circuit**, 
varying  in  circumference  from  100  to  1800  miles.  The  lines  are  so 
interlaced  that  each  line  usually  forms  a  part  of  two  circuits.  The 
greatest  error  indicated  by  the  circuit  closures  in  any  line  of  the  whole 
system,  involving  nearly  20000  miles  of  leveling  executed  by  the  Coast 
and  Geodetic  Survey  and  other  organizations,  is  1.8  millimeters  per 
kilometer,  or  about  one-tenth  of  an  inch  per  mile.  On  all  of  the  lines 
run  by  the  method  now  in  use  and  with  such  instruments  as  that 
shown  in  the  illustration,  the  greatest  error  indicated  by  the  circuit 
closures  is  0.074  millimeter  per  kilometer,  or  about  2-5-0  of  an  inch  per 
mile.    The  total  length  of  lines  so  run  is  3400  miles. 

With  the  new  instrument  and  method  the  leveling  has  been  remark- 
ably rapid  and  cheap,  as  well  as  extremely  accurate.  The  average 
rate  of  progress  for  the  first  2400  miles  of  such  leveling  was  66  com- 
pleted miles  per  month,  each  mile  being  leveled  at  least  twice,  once 
in  the  forward  and  once  in  the  backward  direction.  During  the  month 
in  which  the  most  rapid  leveling  was  done,  105  miles  of  the  line  were 
completed,  this  being  223  miles  of  single  line,  or  an  average  of  8.9 


miles  of  single  line  per  working  day.  The  cost  of  this  leveling  has 
been  from  $7  to  $11  per  mile,  or  from  one-fourth  to  one-half  as  much 
as  leveling  of  the  same  grade  of  accuracy  obtained  with  any  other 
instrument  and  method. 

Leveling  by  vertical  angles,  or,  as  it  is  usually  called,  trigonometric 
leveling,  consists  in  measuring  at  any  station  the  angle  of  elevation  or 
depression  of  a  distant  station,  and  is  carried  on  in  connection  with 
triangulation.  The  sight  in  this  case  may  be  of  any  length,  and  in 
mountainous  regions  sometimes  exceeds  100  miles.  The  distance  to 
the  station  sighted  being  known,  the  difference  of  elevation  between 
the  observer's  station  and  the  distant  point  is  computed.  In  making 
the  computations  of  heights  from  such  observations  it  is  necessary  to 
apply  large  corrections,  on  account  of  the  refraction  of  the  ray  of  light 
coming  from  the  distant  point  to  the  observer.  This  refraction  is  quite 
variable,  having  different  values  at  different  hours  of  the  day,  on  dif- 
ferent days  and  in  different  seasons.  Little  is  known  in  regard  to  the 
laws  controlling  the  changes,  and  the  accuracy  of  the  trigonometric 
leveling  falls  considerably  below  that  of  precise  spirit  leveling.  The 
plan  followed  for  preventing  the  accumulation  of  errors  and  improving 
the  elevations  determined  by  trigonometric  leveling  is  to  connect  these 
measures  at  various  points  with  precise  level  bench  marks  and  to 
adjust  the  trigonometric  levels  to  fit  the  precise  leveling  between  these 
points.  When  this  has  been  done  the  resulting  heights  are  of  sufficient 
accuracy  for  mapping  purposes.  Thousands  of  points  have  been  so 
determined  in  various  parts  of  the  LTnited  States.  The  connections 
with  precise  leveling  work  and  other  tests  of  the  accuracy  of  the 
trigonometric  leveling  indicate  that,  roughly  speaking,  it  is  an  even 
chance  that  the  difference  of  elevation  of  two  points  determined  by 
trigonometric  leveling  is  right  within  1  inch  to  the  mile  when  the 
computation  is  made  from  observations  in  both  directions  over  a  single 
line  on  several  days  at  each  station. 

Washington,  D.  C,  April  30,  1904- 


o 


DEPARTMENT  OF   COMMERCE  AND   LABOR 
Coast  and  Geodetic  Survey 


O.  H.  TITTMANN,  Superintendent 


No.  lO 


COAST  PILOTS 


Coast  Pilots  are  compiled  to  assist  mariners  in  the  navigation  of 
their  vessels.  They  serve  to  supplement  the  charts  issued  for  that 
purpose.  The  Coast  Pilots  contain  information  which  is  important  to 
the  mariner  and  which  is  of  such  a  character  that  it  can  not  be  con- 
veniently placed  upon  a  chart.  The  governments  of  the  principal 
maritime  nations  publish  works  for  these  purposes. 

As  early  as  1796  a  volume  known  as  The  American  Coast  Pilot, «  by 
Capt.  Lawrence  Furlong,  was  published  in  Xewburyport,  ^lassa- 
chusetts,  by  Edmund  M.  Blunt,  and  the  first  edition  met  with  so 
ready  a  sale  that  a  second  edition  of  the  same  work  was  published  in 
1798.  Since  the  latter  date  numerous  comjnlers  have  published  Coast 
Pilots  of  the  coast  of  the  United  States  and  its  harbors.     These  works 


a  The  first  Coast  Pilot  published  in  America. 


Ko.  10 


2 

were  compiled  from  charts,  from  reports  by  shipmasters  pu Wished  in 
the  newspapers,  and  from  surveys  and  the  personal  knowledge  of 
the  compilers,  some  of  whom  were  experienced  shipmasters. 

The  vessels  of  the  Coast  and  Geodetic  Survey,  while  engaged  in 
surveying  .the  coast  and  harbors  of  the  United  States,  collect  much 
information  of  importance  to  mariners  which  can  not  be  shown  on  the 
charts  or  completely  given  in  Notices  to  Mariners.  Coast  Pilots  are 
published  and  distributed  by  the  Coast  and  Geodetic  Survey  at  the 
cost  of  the  printing  and  binding.  Similar  information  can  not  be  col- 
lected by  private  enterprise  except  at  great  cost  and  with  imperfect 
means,  and  at  the  present  time  all  the  private  publications  containing 
such  information  relative  to  the  coast  of  the  United  States  are  com- 
pilations from  Government  publications  and  are  generally  based  on 
the  work  of  the  Coast  and  Geodetic  Survey. 

The  compilation  of  the  Coast  Pilots  necessitates  work  in  the  office 
and  in  the  field.  The  oflfice  work  consists  of  the  collection  of  the  lat- 
est data  from  the  reports  and  surveys  of  hydrographic  and  topographic 
parties,  from  the  reports  and  surveys  of  the  United  States  engineers 
engaged  in  the  improvement  of  harbors  and  waterways,  and  from 
correspondence  with  local  authorities  and  engineers.  This  informa- 
tion, in  manuscript,  is  then  put  in  the  form  which  experience  has 
shown  to  be  convenient  for  the  use  of  the  mariner. 

For  the  field  work  a  vessel  of  the  Survey,  with  the  compilers  of  the 
Coast  Pilot  on  board,  visits  every  part  of  the  coast  which  is  treated  in 
the  volume;  the  information  collected  in  the  office  is  verified  and,  if 
necessary,  corrected  on  the  spot;  the  sailing  lines  and  directions  are 
tested  by  running  over  the  courses  given;  such  artificial  aids  and  natu- 
ral landmarks  as  are  of  use  to  the  mariner  are  noted,  and  hydrographic 
examinations  of  reported  dangers  and  changes  are  made;  pilots,  ship- 
masters, and  local  authorites  are  interviewed  and  the  latest  information 
is  incorporated,  together  with  such  notes  as  can  only  be  obtained  by 
observation  and  experience  in  the  locality. 

On  returning  to  the  office  from  the  field,  the  manuscript,  corrected 
to  date,  is  prepared  for  the  printer,  and  when  issued  the  volumes  con- 
tain a  supplement  or  insertion  sheet  of  the  changes  which  have  occurred 
since  the  date  of  the  preparation  of  the  volume  and  while  the  matter 
was  going  through  the  press. 


The  Coast  Pilots  published  by  the  Coast  and  Geodetic  Survey 
contain — 

1.  A  tabular  description  of  lighthouses,  light- vessels,  and  fog  sig- 
nals; lists  of  life-saving  stations,  storm- warning  display  stations,  and 
seacoast  telegraph  stations,  and  information  regarding  tides,  tidal  cur- 
rents, variation  of  the  compass,  etc. 

2.  Xautical  descriptions  of  the  coast  and  harbors  and  general  infor- 
mation concerning  the  several  bodies  of  water  and  harbors,  including 
notes  relative  to  pilots,  depth  of  water,  draft  of  vessels  entering  the 
harbor,  supplies,  facilities  for  making  repairs,  usual  or  best  anchor- 
age, and  other  matters  of  practical  value.  In  each  case  the  informa- 
tion of  this  nature  precedes  the  sailing  directions  and  is  printed  in 
smaller  type. 

3.  Sailing  directions,  with  subordinate  paragraphs  treating  of  prom- 
inent objects,  dangers,  aids  to  navigation,  etc.  The  arrangement  con- 
forms to  the  order  in  which  these  matters  would  be  considered  in 
practice  and  be  available  when  wanted  promptly.  For  this  purpose, 
and  to  afford  a  ready  means  of  reference  from  one  part  to  another,  the 
sailing  directions,  where  Jong,  are  divided  into  numbered  or  lettered 
paragraphs,  printed  in  large  type,  each  followed  by  its  own  subordi- 
nate remarks  in  smaller  type. 

4.  Appendices,  containing  rules  of  the  road  at  sea  and  in  inland 
w^aters,  laws  and  regulations  relative  to  pilotage,  harbor  control, 
national  and  local  quarantine  and  the  Public  Health  and  3Iarine- 
Hospital  Service,  and  information  regarding  storm-warning  displays. 

5.  Views  of  important  points.  These  are  only  inserted  in  volumes 
which  treat  of  localities  which  have  not  yet  been  surveyed  or  where 
the  lighthouses  and  other  aids  to  navigation  are  not  sufficiently 
numerous  to  readily  locate  and  navigate  a  vessel. 

6.  Sections  of  charts,  covering  the  coast  treated  in  the  volume,  to  aid 
in  finding  the  geographic  positions  of  different  localities,  and  index 
maps  showing  the  limits  of  the  charts  covering  the  localities  treated 
in  the  volume. 

The  Coast  Pilot  publications  of  the  Coast  and  Geodetic  Survey 
include — 

Seven  volumes  of  the  United  States  Coast  Pilot,  Atlantic  Coast,  in 
8  parts,  as  follows: 

Parts  I-II.  From  St.  Croix  River  to  Cape  Ann. 

5 


Part  III.  From  Cape  Ann  to  Point  Judith. 

Part  IV.  From  Point  Judith  to  New  York. 

Part  V.  From  New  York  to  Chesapeake  Bay  Entrance. 

Part  A^I.  Chesapeake  Bay  and  Tributaries. 

Part  VII.  From  Chesapeake  Bay  Entrance  to  Key  West. 

Part  VIII.  Gulf  of  Mexico,  from  Key  West  to  the  Rio  Grande. 

One  vohime  of  the  United  States  Coast  Pilot,  Pacific  Coast;  Cali- 
fornia, Oregon  and  Washington. 

One  volume  of  the  United  States  Coast  Pilot,  Pacific  Coast;  Alaska, 
Part  I,  Dixon  Entrance  to  Yakutat  Bay,  with  Inland  Passage  from 
Juan  de  Fuca  Strait  to  Dixon  Entrance. 

In  addition  to  the  above  Coast  Pilots,  bulletins  containing  the  latest 
information  obtainable  from  all  sources  about  the  little-known  waters 
of  northwest  Alaska  and  Bering  Sea  are  published  for  the  use  of 
mariners  navigating  those  waters. 

It  is  manifest  that  publications  of  this  character  must  be  subject  to 
numerous  corrections  in  the  details  after  the  lapse  of  a  few  years.  To 
maintain  the  volume  in  a  useful  form  corrections  are  issued  in  Notices 
to  Mariners,  insertion  sheets,  and  supplements;  and  each  volume  is 
revised  and  passed  to  a  new  edition  when  the  corrections  have  assumed 
proportions  that  impair  its  usefulness,  or  more  recent  surveys  show 
changes  or  furnish  additions  that  render  the  old  volume  unsatisfactory. 

Washington,  D.  C,  April  SO,  1904. 


o 


DEPARTMENT  OF   COMMERCE  AND   LABOR 

Coast  and  Geodetic  Survey 

O.  H.  TITTMANN,  Superintendent 


No.  11 


CHART  PUBLICATIONS 


Charts  are  designed  to  assist  the  navigator  and  to  subserve  the  inter- 
ests of  commerce.  For  purposes  of  navigation  they  may  embrace  large 
areas,  like  one  of  the  great  oceans  or  seas,  delineating  the  conforma- 
tion of  the  shores  and  outlying  dangers,  and  perhaps  indicating  the 
principal  currents  and  winds  that  may  be  utilized  in  determining  the 
most  advantageous  routes  between  specified  localities.  Charts  may 
also  embrace  much  smaller  areas,  but  on  larger  scales,  permitting 
greater  fullness  of  the  detail,  and  thus  presenting  graphically  the 
channels  that  can  be  followed,  with  the  depths  of  the  water,  the  posi- 
tions of  lights,  beacons,  spindles,  buoys,  and  other  objects  provided  to 
indicate  the  way  to  the  stranger.  Charts  of  these  classes  are  usually 
designated  "Navigation  charts,"  although  they  may  also  be  useful  for 
other  purposes. 

No.  11 


All  classes  of  charts  aid  in  the  extension  of  commerce — one  class 
representing  large  areas  as  guides,  and  the  other  class  delineating  lim- 
ited areas,  such  as  harbors,  roadsteads,  and  anchorages,  presenting  all 
the  advantages  and  disadvantages  of  a  locality.  These  harbor  charts 
or  plans  may  exhibit  every  important  detail  of  the  harbor,  and  if 
based  upon  precise  surveys  possess  an  additional  value  to  the  engineer 
for  the  study  of  physical  conditions  with  a  view  to  improvements,  and 
for  defensive  purposes. 

Nearly  all  civilized  nations  have  published  charts  of  their  coast 
lines,  in  greater  or  less  detail,  and  the  principal  maritime  nations  copy 
those  issued  by  other  nations,  and  thus  maintain  for  the  use  of  their 
own  seamen  charts  of  all  parts  of  the  world  to  which  their  commerce 
may  extend.  Great  Britain  maintains  the  most  extensive  establish- 
ment for  the  purpose,  and  issues  the  most  complete  series  of  charts; 
she  has  also  made  the  most  extensive  surveys  of  uncivilized  coasts  for 
cartographic  purposes. 

In  the  United  States  three  bureaus  of  the  Government  service  are 
authorized  to  issue  charts,  but  under  restrictions  intended  to  clearly 
define  the  duties  of  each  and  prevent  unnecessary  duplication — the 
Coast  and  Geodetic  Survey,  in  the  Department  of  Commerce  and 
Labor,  the  Hydrographic  Office,  in  the  Navy  Department,  and  the 
Corps  of  Engineers,  in  the  War  Department.  The  Coast  and  Geo- 
detic Survey  is  charged  with  surveying  the  coasts  of  the  United  States 
and  the  coasts  under  the  jurisdiction  of  the  United  States,  and  with 
researches  to  determine  the  origin  and  courses  of  the  great  ocean  cur- 
rents known  as  the  Gulf  Stream  and  the  Japan  Stream,  and  to  issue 
charts  from  these  surveys  suitable  for  the  purposes  of  navigation, 
commerce,  and  the  public  defense;  the  Hydrographic  Office,  with  the 
duplication  of  charts  and  plans  issued  by  other  nations,  and  the  pub- 
lication of  surveys  by  the  Navy  on  other  coasts  not  under  the  jurisdic- 
tion of  the  United  States;  the  Corps  of  Engineers,  with  survey  of 
the  Great  Lakes  and  the  issue  of  the  charts  necessary  for  their 
navigation. 

The  Coast  and  Geodetic  Survey  issues  four  series  of  charts  on  the 
Atlantic  and  Gulf  coasts  of  the  United  States,  and  three  series  on  the 
Pacific  coast,  designed  to  subserve  the  purposes  for  which  the  Survey 


was  established.  The  first  series  includes  "Sailing  charts,"  which 
embrace  long  stretches  of  coast,  as  from  the  Bay  of  Fundy  to  Cape 
Hatteras,  Chesapeake  Bay  to  the  Bahamas,  etc.,  and  are  intended  to 
serve  for  offshore  navigation,  or  between  the  greater  headlands,  as 
Cape  Cod,  Cape  Hatteras,  etc.,  and 'between  distant  harbors,  as  Boston 
to  Chesapeake  Bay,  Charleston,  etc.  They  show  only  the  outline  of 
the  continent,  the  seacoast  lights,  and  geographic  information  that 
will  be  useful  for  the  purposes  intended.  The  second  series  includes 
' '  General  charts  of  the  coast, ' '  also  designed  for  purposes  of  naviga- 
tion. They  are  on  a  scale  three  times  as  large  as  that  of  the  first  series, 
and  embrace  more  limited  areas,  as  the  Gulf  of  Maine,  Gay  Head  to 
Cape  Henlopen,  Galveston  to  the  Rio  Grande,  etc.  These  charts  serve 
the  navigator  in  coasting  alongshore  between  headlands,  and  in 
approaching  harbors.  Those  of  the  third  series,  called  "Coast 
charts,"  embrace  the  whole  coast  on  a  uniform  scale  five  times  as 
large  as  that  of  the  second  series.  Such  charts  are  necessarily  confined 
to  comparatively  short  stretches  of  coast,  as  Sandy  Hook  to  Barnegat, 
the  entrance  to  Chesapeake  Bay,  Mobile  Bay,  etc.  One  inch  on  the 
paper  represents  about  1^  statute  miles,  a  scale  sufiiciently  large  to 
give  the  features  of  the  topography  and  hydrography  with  great  clear- 
ness, portraying  the  appearance  of  the  coast  and  the  irregularities  of 
the  bottom  with  a  detail  quite  close  enough  for  the  navigation  of  the 
principal  harbors.  The  fourth  series  consists  of  harbor  charts  on 
large  scales,  intended  to  meet  the  needs  of  local  navigation.  On  the 
Pacific  coast  the  first  series  is  similar  to  that  on  the  Atlantic  coast, 
and  extends  from  San  Diego,  California,  to  Point  Barrow,  Alaska. 
The  second  series  is  on  a  scale  about  six  times  as  large  as  the  first, 
and  is  suitable  for  alongshore  navigation,  and  the  inland  passages  of 
southeast  Alaska.  The  third  series  includes  charts  on  scales  like 
those  of  the  fourth  series  on  the  Atlantic  coast. 

All  these  series  of  charts  are  published  from  the  same  original 
surveys,  the  details  of  the  original  work  being  generalized  or  omitted 
to  meet  the  requirements  any  particular  series  is  intended  to  sub- 
serve. Various  methods  are  available  for  producing  charts  of  these 
classes,  but  experience  has  demonstrated  that  on  coasts  like  large  por- 
tions of  those  of  the   United   States,  which  are  subject  to  frequent 


changes  from  natural  causes,  necessitating  extensive  corrections,  en- 
gravings upon  copper  are  the  most  expedient  and  economical.  The 
engravings  afford  the  additional  advantage  of  being  readily  duplicated 
by  the  electrotyping  process.  All  the  standard  charts  issued  by  the 
bureau  are  therefore  copperplate  engravings.  Preliminary  editions, 
however,  are  frequently  issued  by  means  of  the  "  photolithograph 
process,"  which  affords  a  cheap  and  ready  method  for  temporary 
purposes. 

The  Coast  and  Geodetic  Survey  publishes  about  500  charts,  with  an 
annual  issue  of  97,000  copies. 

Washington,  D.  C,  April  30,  1904. 


0 


DEPARTMENT  OF  COMMERCE  AND   LABOR 
Coast  and  Geodetic  Survey 

O.  H.  TITTMANN,  Superintendent 


No.  12 

GRAVITY 


The  measurement  of  the  force  of  gravity  is  effected  by  means  of  a 
penduhim.  Other  means  have  been  employed,  l)ut  the  pendulum 
furnishes  the  most  precise  as  well  as  the  most  convenient  way.  Ever 
since  Bouguer  made  his  famous  experiment  at  Quito,  one  hundred  and 
sixty  years  ago,  where  a  simple  piece  of  brass  was  suspended  by  a 
thread  of  the  aloe,  the  form  of  the  instrument  has  undergone  succes- 
sive improvements  until  we  now  have  a  modern  type  which  is  com- 
pact, very  portable,  and  of  the  highest  degree  of  precision. 

In  passing  let  it  be  remarked  that  the  first  experimental  proof  of 
the  circumpolar  flattening  of  the  earth  was  obtained  by  counting  the 
oscillations  of  a  pendulum  in  different  latitudes,  and  that  this  opera- 
tion still  holds  its  supremacy  as  the  best  method  of  determining  this 
important  quantity.  Not  only  do  the  observations  accord  well  with 
one  another,  but  the  results  by  other  methods  are  coming  more  and 
more  toward  the  form  set  by  the  pendulum. 

No.  12 


Nearly  every  nation  of  importance  has  made  gravity  work  the  sub- 
ject of  study,  and  different  shapes  have  been  given  to  the  instrument, 
according  to  the  oVjject  in  view  and  the  degree  of  precision  sought. 
Omitting  the  earher  experiments,  the  most  prominent  types  are  the 
invariable  pendulums  used  by  the  English,  French,  and  Kussians  for 
measuring  differences  in  the  force  of  gravity  and  the  reversible  ones 
used  by  the  Germans  for  absolute  determinations.  The  short  forms, 
which  have  as  yet  only  been  employed  for  relative  work,  have  been 
adopted  by  the  Coast  and  Geodetic  Survey  and  are  employed  by  the 
Austrians. 

The  following  is  a  brief  statement  of  the  characteristics  of  the  differ- 
ent types. 

The  Repsold  reversible  pendulum  is  designed  to  measure  the 
absolute  force  of  gravity  and  at  the  same  time  may  be  used  differen- 
tially. It  is  made  of  brass,  and  consists  of  a  hollow  tube  supporting  a 
bob  at  each  end.  The  distance  between  the  two  points  of  suspension 
is  one  meter,  and  the  distribution  of  matter  in  the  instrument  is  such 
that  the  time  of  oscillation  is  the  same  whether  the  pendulum  is  sup- 
ported at  one  point  or  at  the  other.  The  supporting  parts  consist  of  s 
steel  plane  upon  which  the  instrument  rests,  and  a  beveled  piece, 
also  of  steel,  firmly  attached  to  the  pendulum.  These  beveled  pieces 
are  called  the  ''knives,"  and  are,  of  course,  similiar  in  construction  for 
both  points  of  suspension.  Indeed,  they  are  so  made  that  they  may 
be  used  interchangeably,  and  thus  eliminate  sources  of  error.  The 
external  form  of  the  pendulum  is  perfectly  symmetrical  with  refer- 
ence to  the  center  of  figure,  so  that  the  resistance  offered  by  the  air  is 
the  same  for  either  position.  This  is  one  of  the  strong  points  of  this 
form  of  instrument,  as  the  atmospheric  correction  is  a  very  important 
quantity,  and  one  that  has  given  considerable  trouble  in  dealing  with 
absolute  measures  of  gravity.  The  most  prominent  defect  of  the 
Repsold  apparatus  is  that  the  tripod  is  weak  and  is  set  in  vibration 
by  the  movement  of  the  pendulum;  moreover,  the  shape  of  the  latter 
is  such  that  the  air  resistance,  although  the  same  for  both  positions, 
is  too  great.  The  accuracy  of  the  determination  of  the  time  of  one 
oscillation  depends  j)artly  on  the  length  of  time  that  the  pendulum 
will  swing  before  coming  to  rest,  and  in  this  respect  Repsold' s  pendu- 
lum attains  a  precision  less  than  half  that  given  by  other  forms. 
Part  of  this  ai)paratus  consists  of  a  comparator  used  in  getting  the  dis- 


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tance  between  the  knives  m  terms  of  a  meter  supported  vertically 
near  by.  To  calculate  the  absolute  force  of  gravity  it  is  of  course 
necessary  to  know  this  distance,  and  it  must  be  determined  with  an 
accuracy  equal  to  that  attained  in  the  determination  of  the  time  of 
oscillation  of  the  pendulum. 

The  Repsold  pendulum  was  supplanted  in  the  Coast  and  Geodetic 
Survey  practice  by  another  pattern,  due  to  C.  S.  Peirce,  Assistant, 
Coast  and  Geodetic  Survey.  This  instrument  was  also  intended  for 
absolute  measures,  but  embodied  several  improvements  on  the  Repsold 
type.  As  in  the  Repsold,  the  material  was  brass  and  the  stem  was 
a  hollow  cylinder,  but  the  external  form  was  less  complicated  and 
its  greater  weight  and  freedom  from  irregularities  enabled  it  to  swing 
four  or  five  hours  before  coming  to  rest.  Two  lengths  of  this  instru- 
ment were  made — one  in  which  the  distance  between  the  knives  was 
a  meter  and  the  other  in  which  it  was  a  yard.  This  supplied  a  new 
method  of  comparing  the  meter  and  yard  through  a  comparison  of 
the  times  of  oscillation  of  the  two  pendulums,  and  a  subsequent  com- 
parison of  the  length  of  the  pendulums  with  the  respective  standards. 

In  1890  a  complete  departure  was  made  in  the  Survey  regarding  the 
form  of  instrument  and  the  method  of  observation.  A  small  pendu- 
lum, one-fourth  of  the  length  of  those  previously  used,  was  constructed 
as  designed  by  Dr.  T.  C.  Mendenhall,  then  Superintendent  of  the  Coast 
and  Geodetic  Survey,  and  an  elegant  method  of  making  the  observa- 
tions, also  suggested  by  him,  permits  the  work  to  be  done  with  ease 
and  accuracy. 

The  metal  used  is  a  composition  of  copper  and  aluminum.  The 
form  is  that  of  a  flat  stem  supporting  a  lenticular  bob.  The  support- 
ing parts  are  of  agate;  in  one  form  the  beveled  piece  attached  to 
the  pendulum  rests  on  a  plane;  in  another  the  plane  is  attached  to 
the  pendulum  and  rests  on  the  beveled  piece  below.  The  pendulum 
swings  in  a  brass  chamber  from  which  the  air  can  be  exhausted  to 
any  pressure  desired.  The  observations  are  made  by  noting  the  time 
of  a  coincidence  between  the  beat  of  the  pendulum  and  that  of  a 
chronometer,  and  the  observation  of  two  such  coincidences  enables 
one  to  deduce  the  period  of  the  pendulum  in  terms  of  that  of  the 
chronometer.  The  pendulum  is  so  made  that  its  period  is  nearly, 
but  not  quite,  equal  to  a  half  second,  so  that  a  coincidence  occurs 
every  five  or  six  minutes.     By  an  ingenious  mechanical  device  a  beam 


of  light  is  thrown  every  second  into  the  pendulum  receiver,  and  there 
falls  upon  two  mirrors,  one  on  the  pendulum  and  the  other  perma- 
nently fixed  by  its  side.  When  the  pendulum  is  hanging  vertically, 
the  two  illuminated  slits,  as  seen  through  the  observing  telescope, 
coincide,  but  in  any  other  position  of  the  pendulum  only  the  one 
reflected  from  the  fixed  mirror  is  seen,  that  from  the  pendulum  mir- 
ror being  thrown  up  and  down,  according  as  the  pendulum  is  on  one 
side  or  the  other  of  its  equilibrium  point.  When  the  pendulum  from 
continued  swinging  has  lost  or  gained  a  whole  vibration  on  the  chro- 
nometer, a  recurrence  of  the  coincidence  takes  place  and  is  observed 
as  before.  The  advantages  of  this  new  apparatus  are  numerous.  The 
support  is  nearly  free  from  flexure,  and  the  swinging  is  done  in  a 
closed  chamber  protected  from  currents  of  air  and  rapid  changes  of 
temperature.  The  observations  are  moreover  easily  made,  the  pendu- 
lums are  very  portable,  and  the  accuracy  attained  is  far  superior  to 
any  hitherto  reached. 

In  order  to  determine  the  force  of  gravity  at  stations  difficult  of 
access  it  is  desirable  to  reduce  the  dimensions  of  the  apparatus,  as  far 
as  this  can  be  done  without  impairing  the  accuracy  of  the  results. 
This  led  to  the  construction,  some  years  ago,  of  pendulums  similar  to 
those  just  described,  but  having  a  period  of  oscillation  of  one-fourth 
of  a  second.  Their  virtual  length  was,  therefore,  one-sixteenth  of 
a  meter,  or,  say,  2^  inches.  The  transportation  of  an  instrument  of 
this  size,  with  necessary  accessories,  is  an  easy  matter,  and  such  a 
pendulum  has  been  swung  on  the  summit  of  several  high  mountains, 
including  Pikes  Peak.  The  deduced  force  of  gravity  agrees  well 
with  that  obtained  by  means  of  the  larger  apparatus. 

Consult:  Volume  VII,  Mem.  Royal  Astronomical  Society. 

Sabine,  Pendulum  Experiments. 

Great  Trigonometrical  Survey  of  India,  Vol.  V. 

Clarke's  Geodesy. 

Bessel's  Pendeluntersuchungen. 

Reports  Coast  and  Geodetic  Survey. 

Comptes-rendus  de  F  Association  Geodesique  Internationale. 
Washington,  D.  C,  April  30,  1904. 


o 


DEPARTMENT  OF  COMMERCE  AND   LABOR 

Coast  and  Geodetic  Survey 

O.  H.  TITTMAN'X,  Superintendent 


No.  13 


GEODESY  OR  MEASUREMENT  OF  THE  EARTH 


It  is  natural  that  from  the  earliest  times  man  should  have  inquired 
and  speculated  about  matters  concerning  the  earth  upon  which  he 
walks  and  on  which  he  spends  his  life,  but  his  first  crude  ideas  about 
its  shape  and  magnitude  were  not  developed  up  to  the  point  of  a  fair 
resemblance  to  the  facts  until  the  civilization  of  the  race  had  already 
grown  old. 

Geodesy  is  a  natural  development  of  the  simpler  operations  of  land 
surveying,  which  may  be  carried  on  without  knowing  that  the  earth  is 
a  sphere.  Land  surveying  was  practiced  from  a  very  ancient  date. 
Thus,  in  a  papyrus  of  a  date  earlier  than  1700  B.  C.  the  author  stated 
that  his  work  was  a  compilation  from  older  manuscripts.  The  notion 
that  the  earth's  surface  could  not  be  a  plane,  but  must  be  curved  like 
the  surface  of  an  immense  ball,  should  have  been  apparent  to  dwellers 
upon  the  seashore;  yet  the  fact  that  the  earth  is,  roughly  speaking, 

No.  13 


spherical  was  not  appreciated  for  many  centuries  after  civilization  had 
developed  to  such  an  extent  that  land  surveying  was  practiced.  The 
step  from  plane  to  spherical  surveying  was  an  important  one,  and  when 
it  was  made,  geodesy,  allied  to  practical  astronomy,  became  an  inde- 
pendent branch  of  science. 

It  is  the  glory  of  the  famous  School  of  Alexandria  to  have  produced, 
shortly  before  the  beginning  of  the  second  century  before  Christ,  the 
first  measure,  and  a  little  later  a  second  measure  of  the  earth's  curva- 
ture—that is,  of  the  radius  of  the  sphere.  It  is  also  remarkable  that  the 
principle  then  employed  is  the  same  that  has  been  used  ever  since, 
althouirh  in  its  application  the  accuracy  has  been  greatly  increased  at 
the  expense  of  the  addition  of  a  great  mass  of  details  in  the  methods. 
Essentially  it  consists  of  measuring  a  long  north  and  south  line  in  feet, 
miles,  meters,  or  some  other  unit  of  length,  and  of  observing  the  alti- 
tude of  the  sun  ^r  of  some  star  as  seen  from  the  two  ends  of  the 
measured  line.  The  difference  of  the  measured  altitudes  gives  the 
curvature  of  this  arc  of  the  great  earth-sphere  expressed,  say,  in 
degrees.  This  being  known,  as  well  as  the  length  of  the  arc,  the 
circumference  or  the  radius  of  the  sphere  can  bo  computed.  After 
these  first  measures  by  the  School  of  Alexandria  a  thousand  years 
passed  before  a  similar  attempt  was  made — this  time  by  the  Arabs  in 
Mesopotamia,  about  825.  This  in  turn  was  followed,  after  another  long 
lapse  of  eight  centuries  extending  through  the  middle  ages,  by  several 
measures  executed  by  different  nations.  The  principle  of  triangulation 
which  is  used  in  the  refined  modern  measures  was  introduced  in  1617. 

Modern  geodesy,  as  i ;  now  exists,  began  with  the  discovery  of  the 
law  of  gravitation  by  Newton  late  in  the  seventeenth  century,  when 
he  proved  that  the  earth,  as  a  revolving  and  not  wholly  rigid  body 
subject  to  its  own  attraction,  must  take  the  form  of  a  slightly  flattened 
sphere.  The  form  thus  indicated  by  theory  was  apparently  contra- 
dicted by  the  measure  of  an  arc  in  France  between  1683  and  1716, 
which  indicated  the  earth  to  be  an  elongated  sphere.  To  settle  the 
matter  two  memorable  expeditions  were  sent  out — one  to  the  equa- 
torial region  of  Peru  (1735-1741)  and  the  other  to  the  polar  region  of 
Lapland  (1736-1737).  Their  work  proved  Newton's  theory  to  be 
correct,  since  they  found  the  length  of  one  degree  to  be  greater,  or,  in 
other  words,  the  arc  flatter,  near  the  pole  than  near  the  equator.     Since 


then,  in  theory  and  in  practice,  geodesy  has  advanced  on  sure  ground 
and  with  ever-increasing  precision  in  its  results. 

Though  the  early  measures  of  the  earth's  curvature  were  made  along 
meridians  only,  the  modern  methods  of  measures  and  computations 
are  such  that  the  measures  made  along  parallels  of  latitude,  or  in  an 
oblique  direction,  as  well  as  those  along  a  meridian,  may  be  utilized 
in  the  determination  of  the  size  and  figure  of  the  earth. 

The  same  instruments  and  methods  of  observing  are  employed  in  a 
triangulation  designed  primarily  as  a  basis  for  accurate  map  making 
as  are  used  in  measuring  an  arc  for  the  purpose  of  determining  the 
earth's  size  and  figure.  Nearly  all  geodetic  arcs  have  been  obtained 
incidentally  during  the  progress  of  surveys  made  chiefly  for  practical 
purposes. 

Since  the  revival  and  spread  of  science  many  surveys  of  countries, 
made  primarily  for  mapping  purposes  and  yielding  incidentally  geo- 
detic arcs,  have  been  carried  out  in  different  parts  of  the  world. 
In  making  these  measures  France,  Great  Britain,  Germany,  Russia, 
and  the  United  States  have  taken  leading  parts.  Among  the  more 
recent  measures  there  may  be  mentioned  the  Anglo-French  arc, 
extending  from  the  northern  j^art  of  the  British  Isles  southward  into 
Africa;  the  great  Russian  arc,  extending  from  the  Arctic  Ocean  to  the 
northern  boundary  of  Turkey;  the  great  Indian  arc,  extending  from 
the  southern  point  of  India  to  the  Himalayas;  the  European  arc  of  a 
parallel,  extending  from  southern  Ireland  eastward  to  central  Russia; 
and  in  the  United  States,  the  transcontinental  arc,  extending  along  the 
thirty-ninth  parallel  from  the  Atlantic  to  the  Pacific  oceans,  and  the 
eastern  oblique  arc,  extending  parallel  to  the  Atlantic  coast  from  Maine 
to  Louisiana.  These  six  arcs  joined  end  to  end  would  reach  about 
two-fifths  of  the  way  around  the  earth. 

The  form  of  the  earth  as  given  by  the  modern  precise  measurement 
is  found  to  be  such  that  with  considerable  exactness  any  section  of  it 
parallel  to  the  equator  is  a  circle  and  any  section  passing  through 
both  poles  is  an  ellipse.  The  dimensions  and  form  of  this  spheroid, 
or  ellipsoid  of  revolution,  as  it  may  be  called  more  accurately,  are 
usually  stated  by  giving  its  equatorial  and  polar  radii  or  diameters. 
The  two  most  notable  computations  of  the  dimensions  of  the  ellipsoid 
are  that  made  by  Bessel  in  1841  and  that  made  by  Clarke  in  1866.  The 
latter  is  used  in  all  the  computations  of  the  Coast  and  Geodetic  Survey. 


The  dimensions  of  the  earth  as  given  by  these  computations  are  as 
follows: 


a.  Equatorial  radius 

b.  Semipolar  axis  . . 

Difference  a-b... 

a-b 

Compression 

a 


Bessel. 
(Meters.) 


6377397 
6356079 
21318 
1 


299. 12 


Clarke. 
(Meters.) 


6378206 
6356584 

21622 

1 


295.0 


Bessel. 
(Engish 
statute 
miles.) 


8962. 72 

3949. 48 

13.25 


Clarke. 

(English 

statute 

miles.) 


3963. 23 

3949. 79 

13.44 


1  statute  mile  =  5280 
feet  =  1609: 347  meters. 


More  recent  measures  are  not  yet  sufficiently  numerous  to  make  it 
certain  which  of  the  two  sets  of  dimensions  given  above  is  most  nearly 
correct.  It  is  probable  that  the  truth  lies  between  them.  To  appre- 
ciate correctly  the  small  amount  of  flattening  at  the  poles  indicated  by 
the  above  figures  it  should  be  noted  that  if  a  globe  approximately  5 
feet  in  diameter  were  constructed  to  scale  to  represent  the  earth 
its  equatorial  diameter  would  be  but  one-fifth  of  an  inch  longer  than 
its  polar  diameter.  To  the  eye  unaided  by  the  use  of  calipers  or  other 
measuring  instruments  this  globe  M'ould  appear  to  be  a  perfect  sphere. 

The  following  brief  statement  gives  some  of  the  most  important 
facts  in  regard  to  the  two  arcs  already  completed  in  the  United  States. 
That  crossing  the  country  along  the  thirty-ninth  parallel  from  Cape 
May,  New  Jersey,  to  Point  Arena,  California,  is  2625  statute  miles 
(4225  kilometers)  long.  The  ten  base  lines  in  this  triangulation  have 
an  aggregate  length  of  53J  miles,  ojie  of  them  being  nearly  11  miles  .in 
length.  Many  of  the  triangle  sides  in  the  Eocky  Mountain  region 
are  over  100  miles  long  and  there  is  one  line  of  183  miles  over  which 
observations  were  made  in  both  directions.  Some  of  the  triangula- 
tion stations  were  more  than  14000  feet  above  the  sea  (4300  meters). 
Many  astronomic  observations  were  necessary  to  fix  the  position  of 
this  arc  upon  the  earth  and  to  determine  the  true  direction  of  the 
lines  of  the  triangulation.  The  latitude  was  determined  accurately 
at  109  stations,  the  longitude  at  29,  and  the  azimuth  or  true  direction 
at  73. 

The  eastern  oblique  arc  extends  from  Calais,  Maine,  to  New  Orleans, 
Louisiana,  a  distance  of  1623  miles  (2612  kilometers).     The  triangu- 


lation  contains  six  base  lines.  The  latitude  was  determined  at  71 
stations,  the  longitude  at  17,  and  the  azimuth  at  56. 

A  powerful  stimulus  to  progress  in  geodesy  was  given  by  the  forma- 
tion of  the  International  Geodetic  Association,  which  was  founded  in 
1861  and  made  international  in  character  in  1886,  and  of  which  the 
United  States  became  a  member  in  1889.  Nearly  all  the  civilized 
countries  are  now  members  of  this  association.  General  meetings  are 
held  at  least  once  in  three  years,  and  the  proceedings  and  publications 
are  widely  disseminated. 

Washington,  D.  C,  April  30^  1904. 

6 

o 


